Finite-dimensional representations for a class of generalized intersection matrix Lie algebras

Abstract

In this paper, we study a class of generalized intersection matrix Lie algebras $\gim(M_n)$, and prove that its every finite-dimensional semi-simple quotient is of type $M(n,\mathbf{a},\mathbf{c},\mathbf{d})$. Particularly, any finite dimensional irreducible $\gim(M_n)$ module must be an irreducible module of $M(n,\mathbf{a},\mathbf{c},\mathbf{d})$ and any finite dimensional irreducible $M(n,\mathbf{a},\mathbf{c},\mathbf{d})$ module must be an irreducible module of $\gim(M_n)$.

19 pages

Cited by in corpus (1)

• A class of Lie algebras arising from intersection matrices