2025/07/01 by Lü, Rencai, You, Xizhou, Zhao, Kaiming
#17B10 #17B20 #17B65 #17B66 #17B68 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2507.00349
For any finite dimensional Lie superalgebra \mathfrakg (maybe a Lie algebra) with an even derivation d and a finite order automorphism σ that commutes with d, we introduce the (d,σ)-twisted Affine-Virasoro superalgebra \mathfrakL=\mathfrakL(\mathfrakg,d,σ) and determine its universal central extension \mathfrakL=\mathfrakL(\mathfrakg,d,σ). This is a huge class of infinite-dimensional Lie superalgebras. Such Lie superalgebras consist of many new and well-known Lie algebras and superalgebras, including the Affine-Virasoro superalgebras, the twisted Heisenberg-Virasoro algebra, the mirror Heisenberg-Virasoro algebra, the W-algebra W(2,2), the gap-p Virasoro algebras, the Fermion-Virasoro algebra, the N=1 BMS superalgebra, the planar Galilean conformal algebra. Then we give the classification of cuspidal A\mathfrakL-modules by using the weighting functor from U(\mathfrakh)-free modules to weight modules. Consequently, we give the classification of simple cuspidal \mathfrakL-modules by using the A-cover method. Finally, all simple quasi-finite modules over \mathfrakL and \mathfrakL are classified. Our results recover many known Lie superalgebra results from mathematics and mathematical physics, and give many new Lie superalgebras.