Author: Laurent Demonet (Bonn) Title: Group actions on generalized cluster categories An idea to categorify skew-symmetrizable cluster algebras is to let finite groups act on some categories which categorify skew-symmetric cluster algebras. We used this idea successfully on the categories of representations of preprojective algebras and obtained categorifications of some cluster algebras coming from Lie theory. In particular, it can be applied to usual cluster categories by using some appropriate exact subcategories of the categories of representations of preprojectives algebras. The aim of this talk is to present some (partial) results about actions on generalized cluster algebras (in the sens of Amiot). ----------------------------------------------------------------------- Author: Lutz Hille (Hamburg) Title: Quiver Representations and the Irreducible Components in the Complement of the Richardson Orbit (joint with Karin Baur) Abstract: We consider a parabolic subgroup in the General Linear Group, such a group is the stabilizer of a flag in a vector space. The parabolic group acts on the Lie algebra of its unipotent radical, consisting of all endomorphisms mapping a vector space in the flag to the next smaller one. This action admits a dense orbit by a classical result of Richardson. We determine the irreducible components of the complement. The main idea behind the solution relates the action to similar questions about quiver representations. In particular, representations of the directed quiver of type A, the corresponding preprojective algebra and representations of the double quiver. --------------------------------------------------------------------- Author: Yong Jiang (Bonn) Title: The elements in crystal bases corresponding to exceptional modules Abstract: Given any finite dimensional hereditary algebra, we have the associated Ringel-Hall algebra. It is well-known that the composition subalgebra provides a realization of the quantum group. We study the elements in the hall algebra corresponding to an exceptional module. In particular, these elements are in the composition subalgebra. We prove that those elements, in the sense of "modulo q", lie in the crystal bases. -------------------------------------------------------------------- Author: Bernard Leclerc (Caen) Title: Unipotent cells in Kac-Moody groups Abstract : This talk will be a preparation for those of Jan Schröer and Christof Geiss. I will review the necessary notions on Kac-Moody algebras and groups, Lusztig's semicanonical bases, and unipotent cells. --------------------------------------------------------------------- Author: Efren Perez-Terrazas Title: Dit-algebras are generically tame Abstract: Let K be a field of zero characteristic and L an algebraic field extension of K. If A is a dit-algebra over K, under some nice assumptions, A^L is a dit-algebra which is generically tame if A is generically tame. Through the Drozd dit-algebra, I obtain applications to finite-dimensional K-algebras. --------------------------------------------------------------------- Author: Markus Reineke (Wuppertal) Title: DT-invariants from quiver moduli Abstract: In a setup of Kontsevich and Soibelman, noncommutative DT invariants are defined by factoring generating functions of Euler characteristics of moduli spaces into Euler products. We study such factorizations for (framed) moduli spaces of stable representations of quivers and derive integrality properties of the resulting DT invariants. --------------------------------------------------------------------- Author: Jan Schroeer Title: Frobenius categories arising in Lie theory Abstract: To each element $w$ of the Weyl group of a quiver, one can associate a Frobenius subcategory $C_w$ of the module category of a preprojective algebra. The categories $C_w$ were defined and studied by Buan, Iyama, Reiten and Todorov, and (for adaptable Weyl group elements) independently by Geiss, Leclerc and the speaker. We will give a Lie theoretic interpretation of $C_w$. This is joint work with Christof Geiss and Bernard Leclerc. ----------------------------------------------------------------------- Author: Dong Yang (Cologne) Title: New realization of cluster tubes Abstract: We prove that certain orbit category of the perfect derived category of the endomorphism algebra of a standard maximal rigid object of a cluster tube is triangulated and is triangle equivalent to the ambient cluster tube. -----------------------------------------------------------------------