The 3-cyclic quantum Weyl algebras, their prime spectra and a classification of simple modules ( is not a root of unity)

  • Volodymyr V. Bavula

    University of Sheffield, Sheffield S3 7RH, UK
The 3-cyclic quantum Weyl algebras, their prime spectra and a classification of simple modules ($q$ is not a root of unity) cover
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Abstract

The 3-cyclic quantum Weyl algebra , where (a ground field), is a quadratic Noetherian domain of Gelfand–Kirillov dimension 3 that is generated by three subalgebras each of them is either a quantum plane or the quantum Weyl algebra. For the algebras , their prime, completely prime, primitive and maximal spectra are described together with containments of prime ideals (the Zariski–Jacobson topology on the spectrum) and simple -modules are classified when is not a root of unity. For each prime ideal, an explicit set of ideal generators is given. The centre of is where is a cubic element. A semisimplicity criterion for the category of finite dimensional -modules is given. Criteria are presented for all ideals of the algebra  to commute and for each ideal of to be a unique product of primes (up to order).

Cite this article

Volodymyr V. Bavula, The 3-cyclic quantum Weyl algebras, their prime spectra and a classification of simple modules ( is not a root of unity). J. Noncommut. Geom. 18 (2024), no. 3, pp. 1041–1079

DOI 10.4171/JNCG/547