Journal of Algebra最新文献_第3页

A topological approach to key polynomials 关键多项式的拓扑方法

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-17 DOI: 10.1016/j.jalgebra.2025.06.046

Enric Nart , Josnei Novacoski , Giulio Peruginelli

{"title":"A topological approach to key polynomials","authors":"Enric Nart , Josnei Novacoski , Giulio Peruginelli","doi":"10.1016/j.jalgebra.2025.06.046","DOIUrl":"10.1016/j.jalgebra.2025.06.046","url":null,"abstract":"<div><div>In this paper we present characterizations of the sets of key polynomials and abstract key polynomials for a valuation μ of <math><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, in terms of (ultrametric) balls in the algebraic closure <math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math> of K with respect to v, a fixed extension of <math><msub><mrow><mi>μ</mi></mrow><mrow><mo>|</mo><mi>K</mi></mrow></msub></math> to <math><mover><mrow><mi>K</mi></mrow><mo>‾</mo></mover></math>. In particular, we show that the ways of augmenting μ, in the sense of Mac Lane, are in one-to-one correspondence with the partition of a fixed closed ball <math><mi>B</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>δ</mi><mo>)</mo></math> associated to μ into the disjoint union of open balls <math><msup><mrow><mi>B</mi></mrow><mrow><mo>∘</mo></mrow></msup><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>δ</mi><mo>)</mo></math>, modulo the action of the decomposition group of v. We also present a similar characterization for the set of limit key polynomials for an increasing family of valuations of <math><mi>K</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"684 ","pages":"Pages 280-307"},"PeriodicalIF":0.8,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144694952","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}

引用次数: 0

Orthogonal determinants of GLn(q) GLn(q)的正交决定因素

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-14 DOI: 10.1016/j.jalgebra.2025.07.005

Linda Hoyer

引用次数: 0

Groups with finitely many isomorphism classes of non-pronormal subgroups 具有有限多个非正规子群同构类的群

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-09 DOI: 10.1016/j.jalgebra.2025.07.004

Fausto De Mari

引用次数: 0

Non-weight modules over the algebra HW(b) 代数HW(b)上的非权模

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-09 DOI: 10.1016/j.jalgebra.2025.07.003

Yan Liu, Yao Ma, Liangyun Chen

引用次数: 0

An interconnection between pre-Lie rings, braces and associative rings 李前环、支撑环和结合环之间的相互连接

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-08 DOI: 10.1016/j.jalgebra.2025.07.002

Agata Smoktunowicz

引用次数: 0

Fundamental polytope for the isometry group of an alcove 凹形的等距群的基本多面体

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-07 DOI: 10.1016/j.jalgebra.2025.06.035

Lucas Seco , Arthur Garnier , Karl-Hermann Neeb

{"title":"Fundamental polytope for the isometry group of an alcove","authors":"Lucas Seco , Arthur Garnier , Karl-Hermann Neeb","doi":"10.1016/j.jalgebra.2025.06.035","DOIUrl":"10.1016/j.jalgebra.2025.06.035","url":null,"abstract":"<div><div>A fundamental alcove <math><mi>A</mi></math> is a tile in a paving of a vector space V by an affine reflection group <math><msub><mrow><mi>W</mi></mrow><mrow><mi>aff</mi></mrow></msub></math>. Its geometry encodes essential features of <math><msub><mrow><mi>W</mi></mrow><mrow><mi>aff</mi></mrow></msub></math>, such as its affine Dynkin diagram <math><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover></math> and fundamental group Ω. In this article we investigate its full isometry group <math><mi>Aut</mi><mo>(</mo><mi>A</mi><mo>)</mo></math>. It is well known that the isometry group of a regular polyhedron is generated by hyperplane reflections on its faces. Being a simplex, an alcove <math><mi>A</mi></math> is the simplest of polyhedra, nevertheless it is seldom a regular one. In our first main result we show that <math><mi>Aut</mi><mo>(</mo><mi>A</mi><mo>)</mo></math> is isomorphic to <math><mi>Aut</mi><mo>(</mo><mover><mrow><mi>D</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo></math>. Building on this connection, we establish that <math><mi>Aut</mi><mo>(</mo><mi>A</mi><mo>)</mo></math> is an abstract Coxeter group, with generators given by affine isometric involutions of the ambient space. Although these involutions are seldom reflections, our second main result leverages them to construct, by slicing the Komrakov–Premet fundamental polytope <math><mi>K</mi></math> for the action of Ω, a family of fundamental polytopes for the action of <math><mi>Aut</mi><mo>(</mo><mi>A</mi><mo>)</mo></math> on <math><mi>A</mi></math>, whose vertices are contained in the vertices of <math><mi>K</mi></math> and whose faces are parametrized by the so-called balanced minuscule roots, which we introduce here. In an appendix, we discuss some related negative results on stratified centralizers and equivariant triangulations.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"683 ","pages":"Pages 633-671"},"PeriodicalIF":0.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632251","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}

引用次数: 0

Entwined comodules and contramodules over coalgebras with several objects: Frobenius, separability and Maschke theorems 具有若干对象的余代数上的纠缠模和控制模：Frobenius定理、可分性定理和Maschke定理

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-07 DOI: 10.1016/j.jalgebra.2025.07.001

Abhishek Banerjee , Surjeet Kour

引用次数: 0

Embedding theorems for algebras with trace 带迹代数的嵌入定理

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-04 DOI: 10.1016/j.jalgebra.2025.06.026

Allan Berele

引用次数: 0

On modular invariants of the truncated polynomial rings in low ranks 低阶截断多项式环的模不变量

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-04 DOI: 10.1016/j.jalgebra.2025.06.034

Le Minh Ha , Nguyen Dang Ho Hai , Nguyen Van Nghia

引用次数: 0

Fast computation of 2-isogenies in dimension 4 and cryptographic applications 4维2-同胚的快速计算及密码学应用

IF 0.8 2区数学

Journal of Algebra Pub Date : 2025-07-03 DOI: 10.1016/j.jalgebra.2025.06.033

Pierrick Dartois

{"title":"Fast computation of 2-isogenies in dimension 4 and cryptographic applications","authors":"Pierrick Dartois","doi":"10.1016/j.jalgebra.2025.06.033","DOIUrl":"10.1016/j.jalgebra.2025.06.033","url":null,"abstract":"<div><div>Dimension 4 isogenies have first been introduced in cryptography for the cryptanalysis of Supersingular Isogeny Diffie-Hellman (SIDH) and have been used constructively in several schemes, including SQIsignHD, a derivative of SQIsign isogeny based signature scheme. Unlike in dimensions 2 and 3, we can no longer rely on the Jacobian model and its derivatives to compute isogenies. In dimension 4 (and higher), we can only use theta-models. Previous works by Romain Cosset, David Lubicz and Damien Robert have focused on the computation of ℓ-isogenies in theta-models of level n coprime to ℓ (which requires to use <math><msup><mrow><mi>n</mi></mrow><mrow><mi>g</mi></mrow></msup></math> coordinates in dimension g). For cryptographic applications, we need to compute chains of 2-isogenies, requiring to use <math><mo>≥</mo><msup><mrow><mn>3</mn></mrow><mrow><mi>g</mi></mrow></msup></math> coordinates in dimension g with state of the art algorithms.</div><div>In this paper, we present algorithms to compute chains of 2-isogenies between abelian varieties of dimension <math><mi>g</mi><mo>≥</mo><mn>1</mn></math> with theta coordinates of level <math><mi>n</mi><mo>=</mo><mn>2</mn></math>, generalizing a previous work by Pierrick Dartois, Luciano Maino, Giacomo Pope and Damien Robert in dimension <math><mi>g</mi><mo>=</mo><mn>2</mn></math>. We propose an implementation of these algorithms in dimension <math><mi>g</mi><mo>=</mo><mn>4</mn></math> to compute endomorphisms of elliptic curve products derived from Kani's lemma with applications to SQIsignHD and SIDH cryptanalysis. We are now able to run a complete key recovery attack on SIDH when the endomorphism ring of the starting curve is unknown within a few seconds on a laptop for all NIST SIKE parameters.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"683 ","pages":"Pages 449-514"},"PeriodicalIF":0.8,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144594923","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}

引用次数: 0