On the exact sequence and variety of polydules

Abstract

Let Λ be a finite-dimensional algebra over an algebraically closed field k. We study variety W Λ d (k) parameterizing Λ-polydules. This variety carries an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We investigate some relation between exact triangle of polydules and variety of polydules.