Representation Theory of a Semisimple Extension of the Takiff Superalgebra

被引：2

作者：

Cheng, Shun-Jen

Coulembier, Kevin ^{[1
]}

机构：

[1] Acad Sinica, Inst Math, Taipei 10617, Taiwan

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年 / 2022卷 / 18期

基金：

澳大利亚研究理事会;

关键词：

LIE-SUPERALGEBRAS; KOSZUL DUALITY; FUNCTORS; ALGEBRA;

D O I：

10.1093/imrn/rnab149

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a semisimple extension of a Takiff superalgebra, which turns out to have a remarkably rich representation theory. We determine the blocks in both the finite-dimensional and BGG module categories and also classify the Borel subalgebras. We further compute all extension groups between two finite-dimensional simple objects and prove that all non-principal blocks in the finite-dimensional module category are Koszul.

引用

页码：14454 / 14495

页数：42

共 35 条

[1]

[Anonymous], 1986, Contemporary Soviet Mathematics

[2]

Balagovic M, 2019, MATH RES LETT, V26, P643, DOI 10.4310/MRL.2019.v26.n3.a2

[3] Koszul duality patterns in representation theory [J].