Non-weight modules over the super-BMS$_3$ algebra

Abstract

In the present paper, a class of non-weight modules over the super-BMS 3 algebras S ǫ (ǫ = 0 or 1 2 ) are constructed. These modules when regarded as S 0 -modules and further restricted as modules over the Cartan subalgebra h are free of rank 1, while when regarded as S 1 2 -modules and further restricted as modules over the Cartan subalgebra H are free of rank 2. We determine the necessary and sufficient conditions for these modules being simple, as well as determining the necessary and sufficient conditions for two S ǫ -modules being isomorphic. At last, we present that these modules constitute a complete classification of free U (h)-modules of rank 1 over S 0 , and also constitute a complete classification of free U (H)-modules of rank 2 over S 1 2 .

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

“…In [5], U(h)modules over the basic Lie superalgebras were investigated, which showed that osp(1|2n) is the only basic Lie superalgebra that admits such modules. The U(h)-free modules on some infinite-dimensional Lie superalgebras such as super-BMS 3 algebras, super-Virasoro algebras, untwisted N = 2 super conformal algebras were respectively studied in [3,21,22]. The aim of the present paper is to classify such modules for the twisted N = 2 superconformal algebras, and we further investigate the relevant twisted modules and weight modules.…”