Journal of Pure and Applied Algebra最新文献

{"title":"Drinfeld super Yangian of the exceptional Lie superalgebra D(2,1;λ)","authors":"Hongda Lin ,&nbsp;Honglian Zhang","doi":"10.1016/j.jpaa.2025.108126","DOIUrl":"10.1016/j.jpaa.2025.108126","url":null,"abstract":"<div><div>In this paper, we establish the first rigorous framework for the Drinfeld super Yangian associated with an exceptional Lie superalgebra, which lacks a classical Lie algebraic counterpart. Specifically, we systematically investigate the Drinfeld presentation and structural properties of the super Yangian associated with the exceptional Lie superalgebra <span><math><mi>D</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>;</mo><mi>λ</mi><mo>)</mo></math></span>. First, we introduce a Drinfeld presentation for the super Yangian associated with the exceptional Lie superalgebra <span><math><mi>D</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>;</mo><mi>λ</mi><mo>)</mo></math></span>, explicitly constructing its current generators and defining relations. A key innovation is the construction of a Poincaré-Birkhoff-Witt (PBW) basis using degeneration techniques from the corresponding quantum loop superalgebra. Furthermore, we demonstrate that the super Yangian possesses a Hopf superalgebra structure, explicitly providing the coproduct, counit, and antipode.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108126"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On radical unitary ideals of rings of integer-valued polynomials","authors":"Carmelo Antonio Finocchiaro ,&nbsp;K. Alan Loper","doi":"10.1016/j.jpaa.2025.108134","DOIUrl":"10.1016/j.jpaa.2025.108134","url":null,"abstract":"<div><div>Let <em>D</em> be a Dedekind domain (not a field) with finite residue fields and let <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> be the ring of integer-valued polynomials over <em>D</em>. We completely classify in topological terms some relevant classes of radical unitary ideals of <span><math><mi>Int</mi><mo>(</mo><mi>D</mi><mo>)</mo></math></span> (and of its overrings). This project strongly extends the classification given in a previous paper and regarding special unitary ideals, precisely the ones lying over a given maximal ideal of <em>D</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108134"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Weight subgroups of quasi-isolated 2-blocks of the Chevalley groups F4(q)","authors":"Jianbei An","doi":"10.1016/j.jpaa.2025.108124","DOIUrl":"10.1016/j.jpaa.2025.108124","url":null,"abstract":"<div><div>We introduce a way to classify weight subgroups of a block. As an application we classified weight subgroups and proved the Alperin weight conjecture for quasi-isolated 2-blocks of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>q</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108124"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Jordan type of full Perazzo algebras","authors":"Pedro Macias Marques ,&nbsp;Rosa M. Miró-Roig ,&nbsp;Josep Pérez","doi":"10.1016/j.jpaa.2025.108125","DOIUrl":"10.1016/j.jpaa.2025.108125","url":null,"abstract":"<div><div>In this paper, we compute all possible Jordan types of linear forms in any full Perazzo algebra. In some cases we are also able to compute the corresponding Jordan degree-type, which is a finer invariant.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108125"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum vertex algebra associated to quantum toroidal glN","authors":"Fulin Chen ,&nbsp;Xin Huang ,&nbsp;Fei Kong ,&nbsp;Shaobin Tan","doi":"10.1016/j.jpaa.2025.108120","DOIUrl":"10.1016/j.jpaa.2025.108120","url":null,"abstract":"<div><div>In this paper, we associate the quantum toroidal algebra <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> of type <span><math><msub><mrow><mi>gl</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> with quantum vertex algebra through equivariant <em>ϕ</em>-coordinated quasi modules. More precisely, for every <span><math><mi>ℓ</mi><mo>∈</mo><mi>C</mi></math></span>, by deforming the universal affine vertex algebra of <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span>, we construct an <em>ħ</em>-adic quantum <span><math><mi>Z</mi></math></span>-vertex algebra <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mover><mrow><mi>sl</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>ħ</mi></mrow></msub><mo>(</mo><mi>ℓ</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. Then we prove that the category of restricted <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span>-modules of level <em>ℓ</em> is canonically isomorphic to that of equivariant <em>ϕ</em>-coordinated quasi <span><math><msub><mrow><mi>V</mi></mrow><mrow><msub><mrow><mover><mrow><mi>sl</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow><mrow><mo>∞</mo></mrow></msub><mo>,</mo><mi>ħ</mi></mrow></msub><mo>(</mo><mi>ℓ</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>-modules.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108120"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"GAGA type results for singularity categories","authors":"Yilin Wu ,&nbsp;Jinyi Xu ,&nbsp;Guodong Zhou","doi":"10.1016/j.jpaa.2025.108146","DOIUrl":"10.1016/j.jpaa.2025.108146","url":null,"abstract":"<div><div>Several GAGA-type results for singularity categories are presented. Firstly, as an easy consequence of Serre's GAGA theorem, we show that for a complex projective variety, its singularity category is naturally equivalent to that of its analytification.</div><div>Secondly, we introduce the torsion singularity category of a formal scheme. Under Orlov's (ELF) condition, we prove that for the formal completion of a Noetherian scheme along a closed subset, its torsion singularity category is equivalent to the singularity category of the original scheme, with support in the closed subset.</div><div>Lastly, using the Artin Approximation Theorem and the result above, we provide an alternative proof of a result of Orlov. Namely, for a Noetherian local ring with an isolated singularity, its singularity category is equivalent (up to direct summands) to that of its Henselization, which in turn is equivalent to that of its completion.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108146"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Horrocks' theorem for odd orthogonal groups","authors":"A.A. Ambily,&nbsp;H. Sugilesh","doi":"10.1016/j.jpaa.2025.108142","DOIUrl":"10.1016/j.jpaa.2025.108142","url":null,"abstract":"<div><div>We prove Horrocks' theorem for the odd elementary orthogonal group, which gives a decomposition of an orthogonal matrix with entries from a polynomial ring <span><math><mi>R</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span>, over a commutative ring <em>R</em> in which 2 is invertible, as a product of an orthogonal matrix with entries in <em>R</em> and an elementary orthogonal matrix with entries from <span><math><mi>R</mi><mo>[</mo><mi>X</mi><mo>]</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108142"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Which categories are varieties of quantitative algebras?","authors":"Jiří Adámek","doi":"10.1016/j.jpaa.2025.108139","DOIUrl":"10.1016/j.jpaa.2025.108139","url":null,"abstract":"<div><div>Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite, regular generator which is regularly projective (its hom-functor preserves regular epimorphisms). We characterize varieties of quantitative algebras of Mardare, Panangaden and Plotkin analogously as metric-enriched categories. We introduce the concept of a subcongruence (a metric-enriched analogue of a congruence) and the corresponding subregular epimorphisms, obtained via colimits of subcongruences. Varieties of quantitative algebras are precisely the metric-enriched categories with effective subcongruences and a subvarietal generator: an abstractly finite, subregular generator which is subregularly projective (its hom-functor preserves subregular epimorphisms).</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108139"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Raney extensions: A pointfree theory of T0 spaces based on canonical extension","authors":"Anna Laura Suarez","doi":"10.1016/j.jpaa.2025.108137","DOIUrl":"10.1016/j.jpaa.2025.108137","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We introduce a pointfree version of Raney duality. Our objects are &lt;em&gt;Raney extensions&lt;/em&gt; of frames, pairs &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; where &lt;em&gt;C&lt;/em&gt; is a coframe and &lt;span&gt;&lt;math&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is a subframe that meet-generates it and whose embedding preserves strongly exact meets. We show that there is a dual adjunction between &lt;strong&gt;Raney&lt;/strong&gt; and &lt;strong&gt;Top&lt;/strong&gt;, with all &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; spaces as fixpoints, assigning to a space &lt;em&gt;X&lt;/em&gt; the pair &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, with &lt;span&gt;&lt;math&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; are the intersections of open sets. We show that for every Raney extension &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; there are subcolocale inclusions &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the coframe of fitted sublocales and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the frame of joins of closed sublocales. We thus exhibit a symmetry between these two well-studied structures in pointfree topology. The spectra of these are, respectively, the classical spectrum &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;pt&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; of the underlying frame and its &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; spectrum &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;pt&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. This confirms the view advanced in &lt;span&gt;&lt;span&gt;[9]&lt;/span&gt;&lt;/span&gt; that sobriety and the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; property are mirror images of each other, and suggests that the symmetry above is a pointfree view of it. All Raney extensions satisfy some variation of the properties &lt;em&gt;density&lt;/em&gt; and &lt;em&gt;compactness&lt;/em&gt; from the theory of canonical extensions. We characterize sobriety, the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, and the &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; axioms in terms of density and compactness of &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;U&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We characterize frame morphisms &lt;span&gt;&lt;math&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108137"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On braided Hopf structures on exterior algebras","authors":"Rinat Kashaev ,&nbsp;Vladimir Mangazeev","doi":"10.1016/j.jpaa.2025.108135","DOIUrl":"10.1016/j.jpaa.2025.108135","url":null,"abstract":"<div><div>We show that the exterior algebra of a vector space <em>V</em> of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis.</div><div>A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang–Baxter equation. These solutions are conjectured to give rise to the two-variable Links–Gould polynomial invariants associated with the super-quantum group <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mrow><mi>gl</mi></mrow><mo>(</mo><mi>N</mi><mo>|</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></span>, where <span><math><mi>N</mi><mo>=</mo><mi>dim</mi><mo>⁡</mo><mo>(</mo><mi>V</mi><mo>)</mo></math></span>. We support this conjecture through computations for small values of <em>N</em>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 12","pages":"Article 108135"},"PeriodicalIF":0.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145623947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}