A family of simple non-weight modules over the twisted N=2 superconformal algebra

Authors：Chen, Haibo; Dai, Xiansheng; Liu, Mingqiang^*

Source：Journal of Pure and Applied Algebra, 2022, 226(9): 107030.

DOI：10.1016/j.jpaa.2022.107030

• Twisted N=2 superconformal algebra
• Non-weight module
• Simple module

We construct a class of non-weight modules over the twisted N = 2 superconformal algebra L. Let h = CL0 circle plus CG(0) be the Cartan subalgebra of L, and lett = CL0 be the Cartan subalgebra of even part Lo. These modules over L when restricted to the h are free of rank 1 or when restricted to the t are free of rank 2. We provide the necessary and sufficient conditions for these modules to be simple, and give the necessary and sufficient conditions for two such L-modules to be isomorphic. We also compute the action of an automorphism on them. Moreover, based on the weighting functor introduced in [15], a class of intermediate series modules At(sigma) are obtained.