Frobenius Kernels of Algebraic Supergroups and Steinberg’s Tensor Product Theorem

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-12-04 DOI:10.1007/s10468-023-10240-y

Taiki Shibata

引用次数: 0

Abstract

For a split quasireductive supergroup \(\mathbbm {G}\) defined over a field, we study structure and representation of Frobenius kernels \(\mathbbm {G}_r\) of \(\mathbbm {G}\) and we give a necessary and sufficient condition for \(\mathbbm {G}_r\) to be unimodular in terms of the root system of \(\mathbbm {G}\). We also establish Steinberg’s tensor product theorem for \(\mathbbm {G}\) under some natural assumptions.

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代数超群的Frobenius核与Steinberg张量积定理

对于定义在一个域上的分裂拟约超群\(\mathbbm {G}\)，研究了\(\mathbbm {G}\)的Frobenius核\(\mathbbm {G}_r\)的结构和表示，给出了\(\mathbbm {G}_r\)在\(\mathbbm {G}\)的根系统上是非模的充分必要条件。我们还在一些自然假设下建立了\(\mathbbm {G}\)的Steinberg张量积定理。

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

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.