Representations of the small quasi-quantum group

2023/05/10 by Sun Hua, Sun, Hua, Hui-Xiang Chen +3
Materials Science · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Covalent Organic Framework Applications #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2305.06083

openalex publication_date 2023/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the representation theory of the small quantum group U_q and the small quasi-quantum group \widetildeU_q, where q is a primitive n-th root of unity and n>2 is odd. All finite dimensional indecomposable \widetildeU_q-modules are described and classified. Moreover, the decomposition rules for the tensor products of \widetildeU_q-modules are given. Finally, we describe the structures of the projective class ring r_p(\widetildeU_q) and the Green ring r(\widetildeU_q). We show that r(U_q) is isomorphic to a subring of r(\widetildeU_q), and the stable Green rings r_st(\widetildeU_q) and r_st(U_q) are isomorphic.

Related

• Representations of the small quasi-quantum group Qu_q(\mathfraksl₂)
• Representations of little q-Schur algebras
• Exact module categories over Rep(u_q(\mathfraksl₂))
• Monoidal structure of the category of u_q⁺-modules
• Modularization of small quantum groups