论tannakian范畴中扩展的自同态

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-11-07 DOI:10.1017/s0004972723001090

PAYMAN ESKANDARI

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引用次数: 0

摘要

摘要证明了Tannakian范畴中扩展自同态的Schur引理的类似物。更准确地说，设$\mathbf {T}$是特征为零的域上的中性Tannakian范畴。设E是$\mathbf {T}$中A乘以B的扩展。我们考虑了稳定B的E的每一个自同态在$ a \ 0 + $ B上诱导一个标量映射的条件。我们在任意$\mathbf {T}$和E的一般设置下给出了这个方向的结果，然后在$\mathbf {T}$被过滤并且关联到a和B的分级对象满足某些条件时给出了一个更强的结果。我们还讨论了结果的清晰度。

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ON ENDOMORPHISMS OF EXTENSIONS IN TANNAKIAN CATEGORIES

Abstract We prove analogues of Schur’s lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $\mathbf {T}$ be a neutral Tannakian category over a field of characteristic zero. Let E be an extension of A by B in $\mathbf {T}$ . We consider conditions under which every endomorphism of E that stabilises B induces a scalar map on $A\oplus B$ . We give a result in this direction in the general setting of arbitrary $\mathbf {T}$ and E , and then a stronger result when $\mathbf {T}$ is filtered and the associated graded objects to A and B satisfy some conditions. We also discuss the sharpness of the results.

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来源期刊

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society