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On biproducts and extensions 关于双积和扩展
arXiv: Rings and Algebras Pub Date : 2020-07-20 DOI: 10.1090/conm/771/15513
Y. Kashina, Yorck Sommerhaeuser
{"title":"On biproducts and extensions","authors":"Y. Kashina, Yorck Sommerhaeuser","doi":"10.1090/conm/771/15513","DOIUrl":"https://doi.org/10.1090/conm/771/15513","url":null,"abstract":"We describe in which ways the Radford biproducts of certain eight-dimensional Yetter-Drinfel'd Hopf algebras over the elementary abelian group of order 4 can be written as extensions of Hopf algebras.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124157380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
O-operators on hom-Lie algebras homo - lie代数上的o算子
arXiv: Rings and Algebras Pub Date : 2020-07-18 DOI: 10.1063/5.0026719
S. K. Mishra, Anita Naolekar
{"title":"O-operators on hom-Lie algebras","authors":"S. K. Mishra, Anita Naolekar","doi":"10.1063/5.0026719","DOIUrl":"https://doi.org/10.1063/5.0026719","url":null,"abstract":"$mathcal{O}$-operators (also known as relative Rota-Baxter operators) on Lie algebras have several applications in integrable systems and the classical Yang-Baxter equations. In this article, we study $mathcal{O}$-operators on hom-Lie algebras. We define cochain complex for $mathcal{O}$-operators on hom-Lie algebras with respect to a representation. Any $mathcal{O}$-operator induces a hom-pre-Lie algebra structure. We express the cochain complex of an $mathcal{O}$-operator in terms of certain hom-Lie algebra cochain complex of the sub-adjacent hom-Lie algebra associated with the induced hom-pre-Lie algebra. If the structure maps in a hom-Lie algebra and its representation are invertible, then we can extend the above cochain complex to a deformation complex for $mathcal{O}$-operators by adding the space of zero cochains. Subsequently, we study linear and formal deformations of $mathcal{O}$-operators on hom-Lie algebras in terms of the deformation cohomology. In the end, we deduce deformations of $s$-Rota-Baxter operators (of weight 0) and skew-symmetric $r$-matrices on hom-Lie algebras as particular cases of $mathcal{O}$-operators on hom-Lie algebras.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134033806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Amalgamation and extensions of summand absorbing modules over a semiring 半环上求和吸收模块的合并和扩展
arXiv: Rings and Algebras Pub Date : 2020-07-13 DOI: 10.1142/S0219498822501249
Z. Izhakian, Manfred Knebusch
{"title":"Amalgamation and extensions of summand absorbing modules over a semiring","authors":"Z. Izhakian, Manfred Knebusch","doi":"10.1142/S0219498822501249","DOIUrl":"https://doi.org/10.1142/S0219498822501249","url":null,"abstract":"A submodule $W$ of $V$ is summand absorbing, if $x + y in W$ implies $x in W, ; y in W $ for any $x, y in V$. Such submodules often appear in modules over (additively) idempotent semirings, particularly in tropical algebra. This paper studies amalgamation and extensions of these submodules, and more generally of upper bound modules.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121666447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Identities in Group Rings, Enveloping Algebras and Poisson Algebras 群环上的恒等式，包络代数与泊松代数
arXiv: Rings and Algebras Pub Date : 2020-07-09 DOI: 10.1007/978-3-030-63111-6_17
V. Petrogradsky
{"title":"Identities in Group Rings, Enveloping Algebras and Poisson Algebras","authors":"V. Petrogradsky","doi":"10.1007/978-3-030-63111-6_17","DOIUrl":"https://doi.org/10.1007/978-3-030-63111-6_17","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126703131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Growth of Differential Identities 微分恒等式的增长
arXiv: Rings and Algebras Pub Date : 2020-07-08 DOI: 10.1007/978-3-030-63111-6_20
C. Rizzo
{"title":"Growth of Differential Identities","authors":"C. Rizzo","doi":"10.1007/978-3-030-63111-6_20","DOIUrl":"https://doi.org/10.1007/978-3-030-63111-6_20","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129118766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Some identities involving (p,q)-Fibonacci and Lucas quaternions 涉及(p,q)-Fibonacci和Lucas四元数的一些恒等式
arXiv: Rings and Algebras Pub Date : 2020-07-06 DOI: 10.31801/CFSUASMAS.696617
Gamaliel Cerda-Morales
{"title":"Some identities involving (p,q)-Fibonacci and Lucas quaternions","authors":"Gamaliel Cerda-Morales","doi":"10.31801/CFSUASMAS.696617","DOIUrl":"https://doi.org/10.31801/CFSUASMAS.696617","url":null,"abstract":"In this study, we firstly examined the Horadam quaternions defined and studied by Halici and Karatas. Then, we used the Binet's formula to show some properties of the (p,q)-Fibonacci and Lucas quaternions. We also give some important identities including these quaternions. In this paper we have also contributed for the study of (p,q)-Fibonacci and Lucas quaternion sequence, deducing some of their identities using the Binet-style formula of Horadam quaternions. It is our intention to continue the study of this type of sequences, exploring some their applications in the science domain.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"202 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115951985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pseudo-Sylvester domains and skew laurent polynomials over firs 伪sylvester定义域和偏劳伦特多项式
arXiv: Rings and Algebras Pub Date : 2020-06-15 DOI: 10.1142/S0219498822501687
Fabian Henneke, D. L'opez-'Alvarez
{"title":"Pseudo-Sylvester domains and skew laurent polynomials over firs","authors":"Fabian Henneke, D. L'opez-'Alvarez","doi":"10.1142/S0219498822501687","DOIUrl":"https://doi.org/10.1142/S0219498822501687","url":null,"abstract":"Building on recent work of Jaikin-Zapirain, we provide a homological criterion for a ring to be a pseudo-Sylvester domain, that is, to admit a non-commutative field of fractions over which all stably full matrices become invertible. We use the criterion to study skew Laurent polynomial rings over free ideal rings (firs). As an application of our methods, we prove that crossed products of division rings with free-by-cyclic and surface groups are pseudo-Sylvester domains unconditionally and Sylvester domains if and only if they admit stably free cancellation. This relies on the recent proof of the Farrell-Jones conjecture for poly-free groups and extends previous results of Linnell-Luck and Jaikin-Zapirain on universal localizations and universal fields of fractions of such crossed products.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117288600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Multiplicative (generalized)-derivations of prime rings that act as $n$-(anti)homomorphisms 充当$n$-(反)同态的素环的乘法(广义)导数
arXiv: Rings and Algebras Pub Date : 2020-06-02 DOI: 10.30970/ms.53.2.125-133
G. Sandhu
{"title":"Multiplicative (generalized)-derivations of prime rings that act as $n$-(anti)homomorphisms","authors":"G. Sandhu","doi":"10.30970/ms.53.2.125-133","DOIUrl":"https://doi.org/10.30970/ms.53.2.125-133","url":null,"abstract":"Let $R$ be a prime ring. In this note, we describe the possible forms of multiplicative (generalized)-derivations of $R$ that act as $n-$homomorphism or $n-$antihomomorphism on nonzero ideals of $R.$ Consequently, from the given results one can easily deduce the results of Gusic cite{Gusic2005}.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115416274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Lie nilpotency index of a modular group algebra 模群代数的李幂零指标
arXiv: Rings and Algebras Pub Date : 2020-06-02 DOI: 10.1142/S1793557121501291
M. Sahai, B. Sharan
{"title":"Lie nilpotency index of a modular group algebra","authors":"M. Sahai, B. Sharan","doi":"10.1142/S1793557121501291","DOIUrl":"https://doi.org/10.1142/S1793557121501291","url":null,"abstract":"In this paper, we classify the modular group algebra $KG$ of a group $G$ over a field $K$ of characteristic $p>0$ having upper Lie nilpotency index $t^{L}(KG)= vert G^{prime}vert - k(p-1) + 1$ for $k=14$ and $15$. Group algebras of upper Lie nilpotency index $vert G^{prime}vert - k(p-1) + 1$ for $kleq 13$, have already been characterized completely.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124880444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Involutive and oriented dendriform algebras 对合和定向树形代数
arXiv: Rings and Algebras Pub Date : 2020-06-02 DOI: 10.1016/j.jalgebra.2021.04.012.
A. Das, R. Saha
{"title":"Involutive and oriented dendriform algebras","authors":"A. Das, R. Saha","doi":"10.1016/j.jalgebra.2021.04.012.","DOIUrl":"https://doi.org/10.1016/j.jalgebra.2021.04.012.","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121436515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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