The equitable q-deformation of sl2

被引：0
作者：
Mukherjee, Snehashis [1 ]
机构：
[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年
关键词：
Equitable q-deformation of sl(2); polynomial identity algebra; simple modules; DISTANCE-REGULAR GRAPHS; LINEAR TRANSFORMATIONS; ALGEBRA; MODULES; PAIRS;
D O I：
10.1142/S0219498826501513
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the algebra U-q(Delta)(sl(2)), which is known as the equitable q-deformation of sl(2). This algebra was introduced in 2005 by Ito et al. Assume that q is a primitive mth root of unity with m >= 3. We prove that U-q(Delta)(sl(2)) becomes a Polynomial Identity (PI) algebra. It was previously known for such algebras, the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of U-q(Delta)(sl(2)), and we classify up to isomorphism the simple U-q(Delta)(sl(2))-modules. We also find the center of U-q(Delta)(sl(2)).
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页数：21
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共 28 条
  • [1] Alnajjar H., Leonard pairs associated with the equitable generators of the quantum algebra Uq(sl<sub>2</sub>), Linear Multilinear Algebra, 59, pp. 1127-1142, (2011)
  • [2] Bavula V. V., Global dimension of generalized Weyl algebras, Representation Theory of Algebras (Cocoyoc, 1994), CMS Conference Proceedings, 18, pp. 81-107, (1996)
  • [3] Bavula V. V., Description of bi-quadratic algebras on 3 generators with PBW basis, J. Algebra, 631, pp. 695-730, (2023)
  • [4] Bavula V. V., The 3-cyclic quantum Weyl algebras, their prime spectra and a classification of simple modules (q is not a root of unity), J. Noncommut. Geom, 18, (2024)
  • [5] Benkart G., Terwilliger P., The equitable basis for sl<sub>2</sub>, Math. Z, 268, pp. 535-557, (2011)
  • [6] Brown K. A., Goodearl K. R., Lectures on Algebraic Quantum Groups, Advanced Courses in Mathematics CRM Barcelona, (2002)
  • [7] Chari V., Pressley A., A Guide to Quantum Groups, (1994)
  • [8] De Concini C., Procesi C., Quantum groups, D-modules, Representation Theory, and Quantum Groups, Lecture Notes in Mathematics, 1565, pp. 31-140, (1993)
  • [9] Funk-Neubauer D., Tridiagonal pairs and the q-tetrahedron algebra, Linear Algebra Appl, 431, pp. 903-925, (2009)
  • [10] Funk-Neubauer D., Bidiagonal pairs, the Lie algebra sl<sub>2</sub>, and the quantum group Uq(sl<sub>2</sub>), J. Algebra Appl, 12, 5, (2013)
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