Geodesic
Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 253-267.

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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.
DOI : 10.21136/CMJ.2020.0313-19
Classification : 16G20, 17B20, 17B37
Keywords: Heisenberg double; Drinfeld double; derived Hall algebra; Bridgeland's Hall algebra 
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Xu, Fan; Zhang, Haicheng. Drinfeld doubles via derived Hall algebras  and Bridgeland's Hall algebras. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 253-267. doi : 10.21136/CMJ.2020.0313-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0313-19/

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