1. Endomorphisms of Quantum Generalized Weyl Algebras
- Author
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Stéphane Launois and Andrew P. Kitchin
- Subjects
Pure mathematics ,Weyl algebra ,Ring (mathematics) ,Endomorphism ,Laurent polynomial ,Mathematics::Rings and Algebras ,Statistical and Nonlinear Physics ,Mathematics - Rings and Algebras ,Automorphism ,QA150 ,Rings and Algebras (math.RA) ,Simple (abstract algebra) ,Mathematics - Quantum Algebra ,FOS: Mathematics ,Quantum Algebra (math.QA) ,QA ,Mathematics::Representation Theory ,Commutative property ,Quotient ,Mathematical Physics ,Mathematics - 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
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