A realisation of the Bershadsky-Polyakov algebras and their relaxed modules

被引：18

作者：

Adamovic, Drazen ^{[1
]}

Kawasetsu, Kazuya ^{[2
]}

Ridout, David ^{[3
]}

机构：

[1] Univ Zagreb, Fac Sci, Dept Math, Bijenicka 30, Zagreb, Croatia

[2] Kumamoto Univ, Prior Org Innovat & Excellence, Kumamoto 8608555, Japan

[3] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2021年 / 111卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

Vertex operator algebras; W-algebras; Lattice vertex algebras; Relaxed highest-weight modules;

D O I：

10.1007/s11005-021-01378-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a realisation of the universal/simple Bershadsky-Polyakov vertex algebras as subalgebras of the tensor product of the universal/simple Zamolodchikov vertex algebras and an isotropic lattice vertex algebra. This generalises the realisation of the universal/simple affine vertex algebras associated to sl(2) and osp(1 vertical bar 2) given in Adamovic (Commun Math Phys 366:1025-1067, 2019). Relaxed highest-weight modules are likewise constructed, conditions for their irreducibility are established, and their characters are explicitly computed, generalising the character formulae of Kawasetsu and Ridout (Commun Math Phys 368:627-663, 2019).

引用

页数：30

共 54 条

[1]

Adamovic D., 2021, J ALGEBRA APPL, V20

[2]

Adamovic D, REALIZATIONS L K SL

[3]

Adamovic D., UNPUB

[4] On fusion rules and intertwining operators for the Weyl vertex algebra [J].