Finite-dimensional Representations for a Class of Generalized Intersection Matrix Lie Algebras

Abstract

In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(M_n), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(M_n) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(M_n).

Key Words:

• Affine Lie algebras
• Intersection matrix algebras
• Irreducible modules
• Quotient algebras

2000 Mathematics Subject Classification:

• 17B05
• 17B10
• 17B65

ACKNOWLEDGMENTS

The first author is partially supported by NSERC of Canada. The second author is supported by the NNSF of China (Grant No. 11271131).