Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 71, No. 1, pp. 253-267, 2021

Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras

Fan Xu, Haicheng Zhang

Received July 16, 2019. Published online October 20, 2020.

Abstract: Let ${\cal A}$ be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev's theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of ${\cal A}$ via its derived Hall algebra and Bridgeland's Hall algebra of $m$-cyclic complexes.

Keywords: Heisenberg double; Drinfeld double; derived Hall algebra; Bridgeland's Hall algebra

Classification MSC: 16G20, 17B20, 17B37

DOI: 10.21136/CMJ.2020.0313-19

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Fan Xu, Department of Mathematical Sciences, Tsinghua University, Zhongguancun N St, Haidian District, Beijing 100084, P. R. China, e-mail: fanxu@mail.tsinghua.edu.cn; Haicheng Zhang (correspondig author), Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, No.1 Wenyuan Road, Qixia District, Nanjing 210023, P. R. China, e-mail: zhanghc@njnu.edu.cn

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