Representations of the Fermion-Virasoro algebras

2023/06/27 by Yaohui Xue, Kaiming Zhao, Xue, Yaohui +1 · 1 citation
Materials Science · Mathematics · #17B10 #17B65 #17B66 #17B68 #17B81 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Porphyrin and Phthalocyanine Chemistry #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2306.15250

openalex publication_date 2023/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let δ=0 or (1)/(2). In this paper, we introduce the Fermion algebra F(δ) and the Fermion-Virasoro algebra \mathcal S(δ). They are infinite-dimensional Lie superalgebras. All simple smooth F(δ)-modules, all simple weight F(δ)-modules, all simple smooth \mathcal S(δ)-modules of nonzero level, and all simple Harish-Chandra \mathcal S(δ)-modules are determined. Surprisingly, we have found four different \mathcal S(δ)-module structures on free \mathbb C[L₀]-modules of rank 2.

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• (d,σ)-twisted Affine-Virasoro superalgebras

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