Presentations for small reflection equation algebras of type A

Cooke, Juliet; Laugwitz, Robert

Abstract

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type GLn and SLn, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of gln and sln. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types GLn and SLn by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately defined integral forms of these algebras.

Citation

Cooke, J., & Laugwitz, R. (2025). Presentations for small reflection equation algebras of type A. Journal of Algebra, 682, 131-187. https://doi.org/10.1016/j.jalgebra.2025.05.037

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2025
• Online Publication Date: Jun 17, 2025
• Publication Date: Nov 15, 2025
• Deposit Date: Jul 18, 2025
• Publicly Available Date: Jul 18, 2025
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 1090-266X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 682
• Pages: 131-187
• DOI: https://doi.org/10.1016/j.jalgebra.2025.05.037
• Keywords: Reflection equation algebra; Covariantized Hopf algebra; Small quantum group
• Public URL: https://nottingham-repository.worktribe.com/output/51621634
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0021869325003424