A Note on Odd Periodic derived Hall algebras
- Resource Type
- Working Paper
- Authors
- Zhang, Haicheng; Zhang, Xinran; Zhu, Zhiwei
- Source
- Subject
- Mathematics - Representation Theory
Mathematics - Quantum Algebra
Mathematics - Rings and Algebras
- Language
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.
Comment: 14 pages; To appear in Journal of Algebra and Its Applications