The Weyl algebra and its friends: a survey

2023/05/02 by Gaddis, Jason · 2 citations
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2305.01609

Abstract

We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties, representation theory, and invariant theory.

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• Subcategories of Module Categories via Restricted Yoneda Embeddings
• Galois Rings, Coulomb branches and the Gelfand-Kirillov Conjecture

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• Twisted Weyl algebras, crossed products, and representations
• Quantum Weyl algebras
• Isomorphisms between quantum generalized Weyl algebras
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• A Parametric Family of Subalgebras of the Weyl Algebra III. Derivations