Hall algebras associated to root categories

2022/10/22 by Haicheng Zhang, Zhang, Haicheng
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2210.12351

openalex publication_date 2022/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathcal A be a finitary hereditary abelian category. We define a Hall algebra for the root category of \mathcal A by applying the derived Hall numbers of the bounded derived category D^b(\mathcal A), which is proved to be isomorphic to the Drinfeld double Hall algebra of \mathcal A. In the appendix, we also define the 1-periodic derived Hall algebra via the derived Hall numbers of D^b(\mathcal A).

Related

• Derived Hall algebras of root categories
• Periodic derived Hall algebras of hereditary abelian categories
• Derived Hall Algebras
• A Note on Odd Periodic derived Hall algebras
• Double Hall algebras and derived equivalences