Non-weight modules over algebras related to the 2d supersymmetric Galilean conformal algebra

2026/07/22 by Ying Song, Yu-Feng Yao
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · doi:10.1080/00927872.2026.2692638

Abstract

In this paper, we prove that free U(h)-modules of rank 1 and 2 over the two dimensional supersymmetric Galilean conformal algebras SGCA do not exist, where h is the Cartan subalgebra of SGCA. We then construct a family of non-weight modules over the even part of SGCA which is the tensor product of the Heisenberg-Virasoro algebra and C[t]/(t2). Those modules when regarded as modules over the Cartan subalgebra h are free of rank 1. Moreover, we give a classification of the isomorphism classes of such modules.

Citations

• Non-weight representations of Cartan type S Lie algebras
• On non-weight representations of the N = 2 superconformal algebras
• A family of simple non-weight modules over the twisted N = 2 superconformal algebra
• Non-weight representations of Cartan type H Lie algebras

Related

• On non-weight representations of the N=2 superconformal algebras
• Non-weight modules over generalized Heisenberg-Virasoro algebra of rank two
• Tensor product modules over the planar Galilean conformal algebra from free modules of rank one
• A family of simple non-weight modules over the twisted N=2 superconformal algebra
• Simple modules of the planar Galilean conformal algebra from tensor products