U_q(sl₂) at fourth root of unity

1999/12/22 by D. Kastler, Daniel Kastler, Thomas Krajewski +8
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9912185

24 pages, talk presented by Daniel Kastler at the conference "Analysis on infinite-dimensional Lie groups and algebras", Marseille, September 1997

arxiv created 1999/12/22 · openalex publication_date 1999/12/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study finite dimensional quotients of the Hopf algebra U_q(sl₂) at fourth root of unity. We give explicitly all the corresponding automorphisms, real forms and idempotents.

Related

• A diagrammatic definition of U_q(sl₂)
• A new aspect of representations of U_q( sl₂) - root of unity case
• U_q⁺(B₂) and its representations
• Evaluable Jones-Wenzl idempotents at root of unity and modular\n representation on the center of U_qsl(2)
• The positive even subalgebra of U_q(\mathfraksl₂) and its finite-dimensional irreducible modules