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arXiv · 2412.00841

Semi-derived Ringel-Hall bialgebras

Yiyu Li·Liangang Peng
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Abstract

Let $\mathcal{A}$ be an arbitrary hereditary abelian category. Lu and Peng defined the semi-derived Ringel-Hall algebra $SH(\mathcal{A})$ of $\mathcal{A}$ and proved that $SH(\mathcal{A})$ has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of $\mathcal{A}$. In this paper, we introduce a coproduct formula on $SH(\mathcal{A})$ with respect to the basis of $SH(\mathcal{A})$ and prove that this coproduct is compatible with the product of $SH(\mathcal{A})$, thereby the semi-derived Ringel-Hall algebra of $\mathcal{A}$ is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of $\mathcal{A}$.

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Yiyu Li, Liangang Peng. 2024-12-01. Semi-derived Ringel-Hall bialgebras. https://arxiv.org/abs/2412.00841

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