Modules for loop Affine-Virasoro Algebras

2019/07/20 by S. Eswara Rao, Rao, S. Eswara · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1907.08832

openalex publication_date 2019/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the representations of loop Affine-Virasoro Algebras. As they have canonical triangular decomposition, we define Verma modules and its irreducible quotients. We give necessary and sufficient condition for an irreducible highest weight module to have finite dimensional weight spaces. We prove that an irreducible integrable module is either an highest weight module or a lowest weight module whenever the canonical central element acts non trivially. At the end we construct Affine central operators for each integer and they commute with the action of the Affine Lie Algebra.

Citations

• Complete reducibility of integrable modules for the affine Lie (super)algebras

Cited by

• Uniformly bounded weight modules for Map extended Special and Map extended Hamiltonian Lie algebras
• (d,σ)-twisted Affine-Virasoro superalgebras

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