Work

Classification of irreducible integrable representations of loop toroidal Lie algebras

Year: 2025

Type: article

Abstract: The aim of this paper is to classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. Loop toroidal Lie algebras are given by [Formula: see text], where [Formula: see text] is a toroidal Lie algebra, [Formula: see text] is a commutative, associative, finitely generated unital algebra over [Formula: see text] and [Formula: see text] is the space spanned by degree derivations [Formula: see text] over [Formula: see text]. When the center of toroidal Lie algebra acts non-trivially on modules, we prove that modules come from direct sum of finitely many copies of affine Kac–Moody Lie algebras. In the case when the center of toroidal Lie algebra acts trivially on modules, we prove modules come from direct sum of finitely many copies of finite dimensional simple Lie algebras.

Source: Journal of Algebra and Its Applications

DOI: 10.1142/s0219498827500770

Authors: Priyanshu Chakraborty, Punita Batra

Institutions: Homi Bhabha National Institute, Harish-Chandra Research Institute

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Department of Atomic Energy, Government of India

OpenAlex ID: W3041563343

FWCI:

Cites: 8

Cited by:

Related to: 20