The Periplectic Brauer Algebra III: The Deligne Category

被引：7
|
作者：
Coulembier, Kevin [1 ]
Ehrig, Michael [2 ]
机构：
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100488, Fangshan Distri, Peoples R China
来源：
ALGEBRAS AND REPRESENTATION THEORY | 2021年 / 24卷 / 04期
基金：
澳大利亚研究理事会;
关键词：
Deligne category; Thick tensor ideals; Periplectic Lie superalgebra; Categorification; Diagram algebras; Temperley-Lieb algebra; Fock space; REPRESENTATIONS; FUNCTORS; IDEALS;
D O I：
10.1007/s10468-020-09976-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne's universal monoidal category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne category. This allows us to determine the objects in the kernel of the monoidal functor going to the module category of the periplectic Lie supergroup. We use this to classify indecomposable direct summands in the tensor powers of the natural representation, determine which are projective and determine their simple top.
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页码：993 / 1027
页数：35
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