Abstract
The aim of the paper is to introduce new large classes of algebras—quiver generalized Weyl algebras, skew category algebras, diskew polynomial rings and skew semi-Laurent polynomial rings.
Article PDF
Similar content being viewed by others
References
Bavula, V.V.: Finite-dimensionality of \({{\rm Ext}}^n\) and \({{\rm Tor}}_n\) of simple modules over a class of algebras. Funct. Anal. Appl. 25(3), 229–230 (1991)
Bavula, V.V.: Classification of simple \({{\rm sl}}(2)\)-modules and the finite-dimensionality of the module of extensions of simple \({{\rm sl}}(2)\)-modules. Ukr. Math. J. 42(9), 1044–1049 (1990)
Bavula, V.V.: Simple \(D[X, Y;\sigma, a]\)-modules. Ukr. Math. J. 44(12), 1500–1511 (1992)
Bavula, V. V.: Generalized Weyl algebras and their representations. (Russian) Algebra i Analiz 4(1), 75–97 (1992); translation in St. Petersburg Math. J.4(1), 71–92 (1993)
Bavula, V.V.: Generalized Weyl algebras, kernel and tensor-simple algebras, their simple modules. In: Representations of Algebras (Ottawa, ON, 1992), Proceedings of CMS Conference, American Mathematical Society, Providence, RI, vol. 14, pp. 83–107 (1993)
Bavula, V.V.: Extreme modules over the Weyl algebra \(A_n\). Ukr. Math. J. 45(9), 1327–1338 (1993)
Bavula, V.V.: Description of two-sided ideals in a class of noncommutative rings. I. Ukr. Math. J. 45(2), 223–234 (1993)
Bavula, V.V.: Description of two-sided ideals in a class of noncommutative rings. II. Ukr. Math. J. 45(3), 329–334 (1993)
Bavula, V.V.: Filter dimension of algebras and modules, a simplicity criterion of generalized Weyl algebras. Commun. Algebra 24(6), 1971–1992 (1996)
Bavula, V. V.: Generalized Weyl algebras and diskew polynomial rings. https://arxiv.org/abs/1612.08941
McConnell, J.C., Robson, J.C.: Noncommutative Noetherian Rings. Wiley, Chichester (1987)
Zachos, C.: Elementary paradigms of quantum algebras. Contemporary Math. 134, 351–377 (1992)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bavula, V.V. Quiver Generalized Weyl Algebras, Skew Category Algebras and Diskew Polynomial Rings. Math.Comput.Sci. 11, 253–268 (2017). https://doi.org/10.1007/s11786-017-0313-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11786-017-0313-5
Keywords
- Skew category algebra
- Quiver generalized Weyl algebra
- Diskew polynomial ring
- Generalized Weyl algebra
- Skew double quiver algebra
- Double quiver groupoid