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arXiv · 2307.09071

A Note on Odd Periodic derived Hall algebras

Haicheng Zhang·Xinran Zhang·Zhiwei Zhu
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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.

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Haicheng Zhang, Xinran Zhang, Zhiwei Zhu. 2023-07-18. A Note on Odd Periodic derived Hall algebras. https://arxiv.org/abs/2307.09071

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