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Non-weight modules over algebras related to the Virasoro algebra. (arXiv:1802.01814v1 [math.RT])
来源于:arXiv
In this paper, we study a class of non-weight modules over two kinds of
algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras
$\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where
$q$ is a nonzero complex number. We determine those modules whose restriction
to the Cartan subalgebra (modulo center) are free of rank one. We also provide
a sufficient and necessary condition for such modules to be simple, and
determine their isomorphism classes. Moreover, we obtain the simplicity of
modules over loop-Virasoro algebras by taking tensor products of some
irreducible modules mentioned above with irreducible highest weight modules or
Whittaker modules. 查看全文>>