Representation Theory Day
Paderborn (February 12, 2009)

Organisation: Paderborn Representation Theory Group

Speakers: Hideto Asashiba (Shizuoka), Zhaoyong Huang (Nanjing), Daniel Murfet (Bonn), Dmitri Orlov (Moskau), Claus Michael Ringel (Bielefeld), Øyvind Solberg (Trondheim)

Registration: There is no formal registration. However, please send a short message to  Ms. K. Bornhorst if you intend to participate.

Accomodation: The recommended place is Hotel Campus Lounge.

Programme

All lectures will be in room D1.303 of the main university building.

Hideto Asashiba:
Covering theory of categories without free actions and colimit orbit categories

Abstract: We fix a commutative ring k and all categories and functors are assumed to be k-linear. Assume that a group G acts on a category C by a monomorphism G --> Aut(C) (:= the group of automorpisms of C). To discuss covering theory it is usually assumed that the G-action on C is free. Here we will show that all the results given by Cibils and Marcos hold without this assumption by introducing a notion of G-covering and by characterizing it.  In particular we see any category with G-action is "weakly G-equivariantly" equivalent to a category with free G-action (liberalization). When G is cyclic, this point of view applies to the setting that G acts on C through the group of auto-equivalences modulo natural isomorphisms to know that the orbit category "C/G" (e.g. a cluster category) is justified by constructing a "colimit orbit category".

Zhaoyong Huang: Higher Auslander algebras admitting trivial maximal orthogonal subcategories

Abstract: Let A be an Artinian higher Auslander algebra admitting a trivial maximal orthogonal subcategory of mod A. Then A is a Nakayama algebra; in particular, if A is an Auslander algebra, then A is a tilted algebra of finite representation type. In the case that A is a finite dimensional algebra, the quiver of A is described explicitly.

Daniel Murfet: Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings

Abstract: I will survey the main results of Buchweitz's unpublished manuscript on the subject of maximal Cohen-Macaulay modules and Tate cohomology. The centerpiece will be the construction, for a Gorenstein ring, of four equivalent triangulated categories. Taking morphism sets in these categories defines a cohomology theory, called Tate cohomology, which reflects stable homological features of the ring.

Dmitri Orlov: Triangulated categories of singularities, D-branes in LG-models and mirror symmetry

Abstract: I am going to talk about triangulated categories of singularities and categories of D-branes of type B in Landau-Ginzburg models and sigma-models. Different properties of these categories will be described. In the end of my talk I am also going to discuss mirror symmetry and a generalized strange Arnold duality.

Claus Michael Ringel: Why are canonical algebras canonical?

Abstract: The first canonical algebras considered were the domestic ones: the denomination "canonical" was intended to select precisely one representative from each derived equivalence class of the Happel-Vossieck list. We are going to collect several properties of these canonical algebras which show the importance of this class of algebras.

Øyvind Solberg: Symmetric algebras with radical cube zero and support varieties

Abstract: We consider the class of symmetric algebras with radical cube zero over an algebraically closed field and investigate when there is a sensible theory of support varieties via the Hochschild cohomology ring of the algebra. This is based on joint work with Karin Erdmann.

Schedule

Thursday, February 12, 2009 (room D1.303)

10.00 - 11.00  Solberg

11.00 - 11.30  Coffee (D2.314)

11.30 - 12.30  Asashiba

12.30 - 13.30  Lunch

13.30 - 14.30  Huang

14.40 - 15.40  Murfet

15.40 - 16.10  Coffee (D2.314)

16.10 - 17.10  Orlov

17.20 - 18.20  Ringel

18.30 Dinner at Restaurant "Belvedere" (Warburger Strasse 91)

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