How to superize \mathfrakgl(∞)

2022/05/14 by George Egorov, Egorov, George
Mathematics · Physics and Astronomy · #17B10 #17B65 #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.2205.07046

openalex publication_date 2022/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Penkov with co-authors stdied several types of Lie algebra \mathfrakgl(∞). Completely different new types of super versions of \mathfrakgl(∞) are introduced in this paper: these are Lie superalgebras of supermatrices infinite in all directions with non-zero elements of each matrix occupying a region around the main diagonal bounded by certain curves, not straight ligns. Several open questions related with further study of the Lie superalgebras introduced and with their possible applications to dynamical systems, such as KdV, are formulated.

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