Simple modules for untwisted affine Lie algebras induced from nilpotent loop subalgebras

2023/10/25 by Volodymyr Mazorchuk, Mazorchuk, Volodymyr · 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.2310.16381

openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module has uncountable dimension and that generic tensor products of these modules are simple.

Cited by

• Whittaker modules over the loop Virasoro algebra
• Simple restricted modules of non-zero level over a deformed Heisenberg-Virasoro algebra

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