Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra

Abstract

In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras related to the Virasoro algebras. We first classify such modules over the Lie algebra $W(\varrho )[s]$ for $s=0,\frac{1}{2}$. With this result and method, we can also do such works for some Lie algebras and superconformal algebras related to the Virasoro algebra, including the several kinds of Schrödinger-Virasoro Lie algebras, which are open up to now.

Latex, 13 pages, Journal of Algebra 2015, In Press. arXiv admin note: text overlap with arXiv:math/0510194 by other authors

References in corpus (6)

• Finite conformal modules over the N=2,3,4 superconformal algebras
• Classification of irreducible Harish-Chandra modules over the loop-Virasoro algebra
• Lie bialgebra structures on the $W$-algebra W(2,2)
• Derivations and automorphisms of twisted deformative Schrödinger-Virasoro Lie algebras
• Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over the Twisted Schrödinger-Virasoro Lie algebra
• Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra