A matrix realization of the quantum group g_{p, q}

2009/04/02 by Yusuke Arike, Arike, Yusuke
Mathematics · #16W35 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:16W35

paper · pdf · doi:10.48550/arxiv.0904.0331

38pages, title changed, Appendix A added, introduction rewritten

openalex publication_date 2009/04/02 · arxiv created 2010/01/23 · arxiv updated 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we will find a matrix realizations of the quantum group g_{p, q}. For this purpose, we construct all primitive idempotents and a basis of g_{p, q}. We determine the action of elements of the basis on the indecomposable projective modules, which give rise to a matrix realization of g_{p, q}. By using this result, we obtain a basis of the space of symmetric linear functions on g_{p, q} and express the symmetric linear functions obtained by the left integral, the balancing element and the center of g_{p, q} in term of this basis.

Citations

• A construction of symmetric linear functions of the restricted quantum group U_q (sl₂)
• The Triplet Vertex Operator Algebra W(p) and the Restricted Quantum Group at Root of Unity

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