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.

Keywords

Generalized intersection matrix / Quantized GIM algebra / Quantum 2-toroidal algebra / Quantum N-toroidal algebra

Funding

National Natural Science Foundation of China(11931009)

Natural Sciences and Engineering Research Council of Canada(11531004)

Simons Foundation(523868)

National Natural Science Foundation of China(11871249)