Tate–Shafarevich groups and algebras

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2023-06-01 DOI:10.1142/s0218196723500364

Boris Kunyavski, Vadim Z. Ostapenko

引用次数: 1

Abstract

The Tate–Shafarevich set of a group [Formula: see text] defined by Takashi Ono coincides, in the case where [Formula: see text] is finite, with the group of outer class-preserving automorphisms of [Formula: see text] introduced by Burnside. We consider analogs of this important group-theoretic object for Lie algebras and associative algebras and establish some new structure properties thereof. We also discuss open problems and eventual generalizations to other algebraic structures.

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Tate-Shafarevich群与代数

Takashi Ono定义的群[公式:见文]的Tate-Shafarevich集合，在[公式:见文]是有限的情况下，与Burnside引入的[公式:见文]的外保类自同构群一致。我们考虑了李代数和结合代数中这一重要群论对象的类似物，并建立了它们的一些新的结构性质。我们也讨论开放问题和最终推广到其他代数结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.