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arXiv · 1311.3907

Endomorphisms of quantum generalized Weyl algebras

A. P. Kitchin·S. Launois
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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 $U_q(\mathfrak{so}_5)$.

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BibTeXRIS

A. P. Kitchin, S. Launois. 2013-11-15. Endomorphisms of quantum generalized Weyl algebras. https://doi.org/10.1007/s11005-014-0691-4

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