Abstract
In this article, the polynomial identity (PI) degree of the multiparameter quantized Weyl algebras have been explicitly computed at roots of unity.
Similar content being viewed by others
References
Akhavizadegan M and Jordan D, Prime ideals of quantized Weyl algebras, Glasgow Math. J. 38(3) (1996) 283–297
Brown K A and Goodearl K R, Lectures on Algebraic Quantum Groups, Advanced Courses in Mathematics CRM Barcelona (2002) (Basel: Birkhäuser Verlag)
Ceken S, Palmieri J H, Wang Y H and Zhang J J, The discriminant criterion and automorphism groups of quantized algebras, Adv. Math. 286 (2016) 754–801
De Concini C and Procesi C, Quantum Groups, in: D-Modules, Representation Theory, and Quantum Groups, Lecture Notes in Mathematics (1993) (Berlin: Springer-Verlag) pp. 31–140
Goodearl K R and Hartwig J T, The isomorphism problem for multiparameter quantized Weyl algebras, São Paulo J. Math. Sci. 9 (2015) 53–61
Goodearl K R, Prime ideals in skew polynomial rings and quantized Weyl algebras, J. Algebra 150(2) (1992) 324–377
Jordan D, A simple localization of the quantized Weyl algebra, J. Algebra 174(1) (1995) 267–281
Leroy A and Matczuk J, On \(q\)-skew iterated Ore extensions satisfying a polynomial identity, J. Algebra Appl. 10(4) (2011) 771–781
Maltsiniotis G, Groupes quantique et structures différentielles, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 831–834
McConnell J C and Robson J C, Noncommutative Noetherian Rings, Graduate Studies in Mathematics 30, (2001) 9Providence, RI: American Mathematical Society)
Newman M, Integral Matrices, Pure and Applied Mathematics 45 (1972) (New York: Academic Press)
Rigal L, Spectre de l’algèbre de Weyl quantique, Beiträge Algebra Geom. 37 (1996) 119–148
Rogers A, Representations of Quantum Nilpotent Algebras at Roots of unity and their completely prime quotients, Ph.D. Thesis (2019) (University of Kent)
Tang X, Automorphisms for some symmetric multiparameter quantized Weyl algebras and their localizations, Algebra Colloq. 24(3) (2017) 419–438
Acknowledgements
The authors would like to thank the National Board of Higher Mathematics, Department of Atomic Energy, Government of India for funding their research. They thank the anonymous referee for carefully reading the paper and for many useful comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: S Viswanath
Rights and permissions
About this article
Cite this article
Bera, S., Mukherjee, S. PI degree of quantized Weyl algebras. Proc Math Sci 133, 18 (2023). https://doi.org/10.1007/s12044-023-00739-1
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12044-023-00739-1