The Parity of Lusztig’s Restriction Functor and Green’s Formula for a Quiver with Automorphism

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-03-04 DOI:10.1007/s10468-025-10324-x

Jiepeng Fang, Yixin Lan, Yumeng Wu

引用次数: 0

Abstract

In Fang et al. (J. Algebra 618, 67–95 2023), Fang-Lan-Xiao proved a formula about Lusztig’s induction and restriction functors which can induce Green’s formula for the path algebra of a quiver over a finite field via the trace map. In this paper, we generalize their formula to that for the mixed semisimple perverse sheaves for a quiver with an automorphism. By applying the trace map, we obtain Green’s formula for any finite-dimensional hereditary algebra over a finite field.

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自同构颤振的Lusztig限制函子和Green公式的宇称性

Fang- lan - xiao在Fang et al. （J. Algebra 618, 67-95 2023）中证明了一个关于Lusztig归纳和限制函子的公式，该公式可以通过迹映射推导出有限域上颤振路径代数的Green公式。在本文中，我们将它们的公式推广到具有自同构颤振的混合半简单逆束的公式。利用迹映射，得到了有限域上任意有限维遗传代数的格林公式。

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.