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Exceptional sequences and Drinfeld double Hall algebras. (English) Zbl 1454.14050

This paper studies the reduced Drinfeld double \(D(\mathcal{A})\) of Ringel-Hall algebra for a finitary hereditary abelian category \(\mathcal{A}\) in the viewpoint of exceptional sequences in \(\mathcal{A}\). The main result is that the subalgebras of \(D(\mathcal{A})\) generated by mutation-equivalent exceptional sequences coincide. The proof is based on some explicit formulas in \(D(\mathcal{A})\) for left and right mutations.

MSC:

14F08 Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16G10 Representations of associative Artinian rings
16G20 Representations of quivers and partially ordered sets
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