Quantum Frobenius Heisenberg categorification

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Brundan, Jonathan¹  Savage, Alistair²  Webster, Ben^3,4 

[1] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

[3] Univ Waterloo, Dept Pure Math, Waterloo, ON, Canada

[4] Perimeter Inst Theoret Phys, Waterloo, ON, Canada

关键词: Categorification;    Frobenius algebra;    Heisenberg algebra;    Monoidal category;    Diagrammatic calculus;   

DOI  :  10.1016/j.jpaa.2021.106792

来源: Elsevier

【 摘 要 】

We associate a diagrammatic monoidal category Heis(k) (A; z, t), which we call the quantum Frobenius Heisenberg category, to a symmetric Frobenius superalgebra A, a central charge k is an element of Z, and invertible parameters z, t in some ground ring. When A is trivial, i.e. it equals the ground ring, these categories recover the quantum Heisenberg categories introduced in our previous work, and when the central charge k is zero they yield generalizations of the affine HOMFLY-PT skein category. By exploiting some natural categorical actions of Heis(k) (A; z, t) on generalized cyclotomic quotients, we prove a basis theorem for morphism spaces. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free