Endomorphisms of quantum generalized Weyl algebras

Abstract

We prove that every endomorphism of a simple quantum generalized Weyl algebra $A$ over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by obtaining an explicit classification of all endomorphisms of $A$. Our main result applies to minimal primitive factors of the quantized enveloping algebra of $U_q({\mathfrak{sl}}_2)$ and certain minimal primitive quotients of the positive part of $U_q({\mathfrak{so}}_5)$.

11 pages

References in corpus (1)

• Endomorphisms of quantized Weyl algebras

Cited by in corpus (1)

• Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra