Hall algebras and quantum groups associated to Dynkin quivers

2016/05/01 by Yun Gao, Limeng Xia, Gao, Yun +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1605.00242

Abstract

For Dynkin quivers, we find the Laurent polynomials \widetildeX_{a, c}^b(v) and use \widetildeX_{a, c}^b(v) to construct the Hall algebra \hc_v(\cc(\cp)) over \mz[v, v^-1], where \widetildeX_{a, c}^b(|\mf_q|)'s are structure constants used by Bridgeland. The Laurent polynomials \widetildeX_{a, c}^b(v) are explicitly given in A₁ case. As an application, we obtain the full quantum groups U_t(\sg) associated to the Dynkin quivers for arbitrary t\not=0,±1.

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