On the center of the small quantum group

2001/07/13 by Anna Lachowska, Lachowska, Anna · 1 citation
Mathematics · #17B #20G #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:17B #msc:20G

paper · pdf · doi:10.48550/arxiv.math/0107098

16 pages

openalex publication_date 2001/07/13 · arxiv created 2002/07/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the quantum Fourier transform F, we describe the block decomposition and multiplicative structure of a subalgebra Z + F(Z) in the center of the small quantum group u_l at a root of unity. It contains the previously known subalgebra Z, which is isomorphic to the algebra of characters of finite dimensional modules over u_l. We prove that the intersection Z ∩ F(Z) coincides with the annihilator of the radical of Z. The whole center of u_l coincides with the obtained subalgebra Z + F(Z) in case of sl₂, and is bigger than that in general.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Cited by

• Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center

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