The Periplectic Brauer Algebra III: The Deligne Category

Kevin Coulembier; Michael Ehrig

doi:10.1007/s10468-020-09976-8

The Periplectic Brauer Algebra III: The Deligne Category

Kevin Coulembier^*, Michael Ehrig

^*Corresponding author for this work

School of Mathematics and Statistics

University of Sydney

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	993-1027
Number of pages	35
Journal	Algebras and Representation Theory
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s10468-020-09976-8
Publication status	Published - Aug 2021

Keywords

Categorification
Deligne category
Diagram algebras
Fock space
Periplectic Lie superalgebra
Temperley-Lieb algebra
Thick tensor ideals

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10.1007/s10468-020-09976-8

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Coulembier, K., & Ehrig, M. (2021). The Periplectic Brauer Algebra III: The Deligne Category. Algebras and Representation Theory, 24(4), 993-1027. https://doi.org/10.1007/s10468-020-09976-8

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AB - 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.

KW - Categorification

KW - Deligne category

KW - Diagram algebras

KW - Fock space

KW - Periplectic Lie superalgebra

KW - Temperley-Lieb algebra

KW - Thick tensor ideals

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JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 4

ER -

The Periplectic Brauer Algebra III: The Deligne Category

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