Bivariant K-theory of generalized Weyl algebras

2018/04/01 by Christian Valqui, Valqui, Christian, Julio Gutiérrez +1
Mathematics · #46L87 (Primary) 19K35 #58B34 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1804.00260

openalex publication_date 2018/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the isomorphism class in \mathfrakKK^alg of all noncommutative generalized Weyl algebras A=\CC[h](σ, P), where σ(h)=qh+h₀ is an automorphism of \CC[h], except when q≠ 1 is a root of unity. In particular, we compute the isomorphism class in \mathfrakKK^alg of the quantum Weyl algebra, the primitive factors B_λ of U(\mathfraksl₂) and the quantum weighted projective lines O(\mathbbWP_q(k, l)).

Related

• Isomorphisms between quantum generalized Weyl algebras
• The Automorphism Groups for a family of Generalized Weyl Algebras
• Bivariant K-theory and the Weyl algebra
• On the automorphisms of quantum Weyl algebras
• Birational Equivalences and Generalized Weyl Algebras