2024/12/01 by Jinrong Wang, Wang, Jinrong, Xiaoqing Yue +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2412.00735
In this paper, firstly we construct two classes of Lie conformal superalgebras denoted by HVS(α) and HVS(β,γ,τ), respectively, where α is an nonzero complex number and β,γ,τ are complex numbers. They are both of rank (2+1) and the even part HVS(α)_0=HVS(β,γ,τ)_0 is the Heisenberg--Virasoro Lie conformal algebra, which is a free ℂ[∂]-module generated by L and H satisfying [LλL]=(∂+2λ)L, [LλH]=(∂+λ)H, [HλH]=0. Then we completely determine the conformal derivations, conformal biderivations, automorphism groups and conformal modules of rank (1+1) for these two Lie conformal superalgebras.