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A Note on Odd Periodic derived Hall algebras (2307.09071v2)
Published 18 Jul 2023 in math.RT, math.QA, and math.RA
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.