Exceptional sequences and Drinfeld double Hall algebras

Shiquan Ruan, Haicheng Zhang

Published 2016-12-29Version 1

Let $\A$ be a finitary hereditary abelian category and $D(\A)$ be its reduced Drinfeld double Hall algebra. By giving explicit formulas in $D(\A)$ for left and right mutations, we show that the subalgebras of $D(\A)$ generated by exceptional sequences are invariant under mutation equivalences. As an application, we obtain that if $\A$ is the category of finite dimensional modules over a finite dimensional hereditary algebra, or the category of coherent sheaves on a weighted projective line, the reduced Drinfeld double composition algebra of $\A$ is generated by any complete exceptional sequence.