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- W2951499356 abstract "In this paper we define the modified Ringel-Hall algebra $cmch(ca)$ of a hereditary abelian category $ca$ from the category $C^b(mathcal{A})$ of bounded $mathbb{Z}$-graded complexes. Two main results have been obtained. One is to give a new proof of Green's formula on Ringel-Hall numbers by using the associative multiplication of the modified Ringel-Hall algebra. The other is to show that in certain twisted cases the derived Hall algebra can be embedded in the modified Ringel-Hall algebra. As a consequence of the second result, we get that in certain twisted cases the modified Ringel-Hall algebra is isomorphic to the tensor algebra of the derived Hall algebra and the torus of acyclic complexes and so the modified Ringel-Hall algebra is invariant under derived equivalences." @default.
- W2951499356 created "2019-06-27" @default.
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- W2951499356 date "2017-07-26" @default.
- W2951499356 modified "2023-09-24" @default.
- W2951499356 title "Modified Ringel-Hall Algebras, Green's formula and Derived Hall Algebras" @default.
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- W2951499356 doi "https://doi.org/10.48550/arxiv.1707.08292" @default.
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