Quantum N-toroidal algebras and extended quantized GIM algebras of N-fold affinization

Abstract

We introduce the notion of quantum $N$-toroidal algebras as natural generalization of the quantum toroidal algebras as well as extended quantized GIM algebras of $N$-fold affinization. We show that the quantum $N$-toroidal algebras are quotients of the extended quantized GIM algebras of $N$-fold affinization, which generalizes a well-known result of Berman and Moody for Lie algebras.