Drinfeld doubles via derived Hall algebras and Bridgeland Hall algebras

2019/01/02 by Xu, Fan, Zhang, Haicheng
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1901.00257

Abstract

Let \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 \A via its derived Hall algebra and Bridgeland Hall algebra of m-cyclic complexes.

Related

• A note on Bridgeland's Hall algebras
• Double Hall algebras and derived equivalences
• Hall algebras associated to root categories
• Derived Hall algebras of root categories
• Bridgeland's Hall algebras and Heisenberg doubles