Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras

2021/01/24 by Yucai Su, Su, Yucai, Xiaoqing Yue +1
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.2101.09707

openalex publication_date 2021/01/24 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28

Abstract

In a previous paper by the authors, we obtain the first example of a finitely freely generated simple \mathbb Z-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper, we obtain, as a byproduct, another class of such Lie conformal algebras by classifying \mathbb Z-graded simple Lie conformal algebras \cal G=⊕_i=-1^∞\cal G_i satisfying the following, (1) \cal G₀≅\rm Vir, the Virasoro conformal algebra; (2) Each \cal G_i for i≥-1 is a \rm Vir-module of rank one. These algebras include some Lie conformal algebras of Block type.

Citations

• Infinite conformal symmetry in two-dimensional quantum field theory

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