Exceptional sequences and Drinfeld double Hall algebras

Abstract

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 double composition algebra of $\A$ is generated by any complete exceptional sequence. Moreover, for the Lie algebra case, we also have paralleled results.

The paralleled results in the Lie algebra case are added

References in corpus (1)

• A note on Bridgeland's Hall algebras

Cited by in corpus (1)

• Applications of mutations in the derived categories of weighted projective lines to Lie and quantum algebras