Classification of Simple Modules of the Ore Extension $$K[X][Y; f\frac{d}{dX}]$$

Author:

Bavula V. V.

Abstract

Abstract For the algebras $$\Lambda $$Λ in the title of the paper, a classification of simple modules is given, an explicit description of the prime and completely prime spectra is obtained, the global and the Krull dimensions of $$\Lambda $$Λ are computed.

Funder

University of Sheffield

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics

Reference11 articles.

1. Bavula, V.V.: The finite-dimensionality of Ext$${}^n$$’s and Tor$${}_n$$’s of simple modules over a class of algebras. Funktion. Anal. i Prilozhen. 25(3), 80–82 (1991)

2. Bavula, V.V.: Generalized Weyl algebras and their representations. Algebra i Analiz 4(1), 75–97 (1992). English transl. in St.Petersburg Math. J. 4(1) (1993), 71–92

3. Bavula, V.V.: Generalized Weyl algebras, kernel and tensor-simple algebras, their simple modules, representations of algebras. In: Dlab, V., Lenzing, H. (eds.) Sixth International Conference, August 19–22, 1992. CMS Conference proceedings, vol. 14, pp. 83–106 (1993)

4. Bavula, V.V.: The simple modules of the ore extensions with coefficients from Dedekind ring. Commun. Algebra 27(6), 2665–2699 (1999)

5. Bavula, V.V., Lu, T.: Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules. J. Math. Phys. 58(1), 011701 (2017). https://doi.org/10.1063/1.4973378

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