A Note on Odd Periodic derived Hall algebras

2023/07/18 by Zhang, Haicheng, Zhang, Xinran, Zhu, Zhiwei
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2307.09071

Abstract

Let m be an odd positive integer and D_m(\mathcal A) be the m-periodic derived category of a finitary hereditary abelian category \mathcal A. In this note, we prove that there is an embedding of algebras from the derived Hall algebra of D_m(\mathcal A) defined by Xu-Chen [13] to the extended derived Hall algebra of D_m(\mathcal A) defined in [16]. This homomorphism is given on basis elements, rather than just on generating elements.

Related

• Periodic derived Hall algebras of hereditary abelian categories
• Hall algebras associated to root categories
• Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories
• Derived Hall Algebras
• Derived Hall algebras of root categories