Bridgeland's Hall algebras and Heisenberg doubles

2017/05/11 by Zhang, Haicheng
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1705.03991

Abstract

Let A be a finite dimensional hereditary algebra over a finite field, and let m be a fixed integer such that m=0 or m>2. In the present paper, we first define an algebra L_m(A) associated to A, called the m-periodic lattice algebra of A, and then prove that it is isomorphic to Bridgeland's Hall algebra \mathcal D\mathcal H_m(A) of m-cyclic complexes over projective A-modules. Moreover, we show that there is an embedding of the Heisenberg double Hall algebra of A into \mathcal D\mathcal H_m(A).

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