Resumen de Polyhedral realization of crystal bases for generalized Kac�Moody algebras

Dong-Uy Shin

• In this paper, we give a polyhedral realization of the crystal B() of Uq�() for the generalized Kac�Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac�Moody algebras of rank 2 and 3, and Monster Lie algebras.