Periodic derived Hall algebras of hereditary abelian categories

2023/03/06 by Zhang, Haicheng · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2303.02912

Abstract

Let m be a positive integer and D_m(\mathcal A) be the m-periodic derived category of a finitary hereditary abelian category \mathcal A. Applying the derived Hall numbers of the bounded derived category D^b(\mathcal A), we define an m-periodic extended derived Hall algebra for D_m(\mathcal A), and use it to give a global, unified and explicit characterization for the algebra structure of Bridgeland's Hall algebra of periodic complexes. Moreover, we also provide an explicit characterization for the odd periodic derived Hall algebra of \mathcal A defined by Xu-Chen [22].

Cited by

• The derived Hall algebra of a graded gentle one-cycle algebra I: the triangle structure

Related

• A Note on Odd Periodic derived Hall algebras
• Hall algebras associated to root categories
• Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories
• Derived Hall Algebras
• Bridgeland's Hall algebras and Heisenberg doubles