Exceptional Sequences in Hall Algebras and Quantum Groups

摘要: Let Λ be a finite-dimensional hereditary algebra over finite field k, \({\mathcal{H}}\)(Λ) and \({\mathcal{C}}\) (Λ) be, respectively, the Hall composition of Λ, \({\mathcal{P}}\) isomorphism classes dimensional Λ-modules I simple Λ-modules. We define δα α δ, in \({\mathcal{P}}\), to right left derivations respectively. By using these action braid group on set exceptional sequences Λ-mod, we provide an effective algorithm calculating root vectors real Schur roots. This means that get inductive method express uλ as combinations elements ui algebra, where i ∈ λ is any Λ-module. Because canonical between Drinfeld–Jimbo quantum generic our applicable directly groups. In particular, all are obtained this way type cases.