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We develop a support theory for elementary supergroup schemes, over a field of positive characteristic p ≥ 3, starting with a definition of a π-point generalising cyclic shifted subgroups of Carlson for elementary abelian groups and π-points of Friedlander and Pevtsova for finite group schemes. These are defined in terms of maps from the graded algebra k[t,τ]/(tp−τ2), where t has even degree and τ has odd degree. The strength of the theory is demonstrated by classifying the parity change invariant localising subcategories of the stable module category of an elementary supergroup scheme. [ABSTRACT FROM AUTHOR]

We present a categorification of the non-crossing partitions given by crystallographic Coxeter groups. This involves a category of certain bilinear lattices, which are essentially determined by a symmetrisable generalised Cartan matrix together with a particular choice of a Coxeter element. Examples arise from Grothendieck groups of hereditary artin algebras. [ABSTRACT FROM AUTHOR]

Abstract: We characterize additive functors which are epimorphisms up to direct factors. [Copyright &y& Elsevier]

Tilting and cotilting modules are classified for the completed path algebra of a quiver of type A˜n with linear orientation. This classification problem arises naturally in the classification of cotilting modules over certain associative algebras (Pacific J. Math. 211 (2003) 41–60). The combinatorics of the collection of all tilting and cotilting modules is described in terms of Stasheff associahedra. [Copyright &y& Elsevier]

We give a short proof of Auslander’s formula relating the covariant and the contravariant defect of a short exact sequence in a module category. An immediate consequence is the classical Auslander–Reiten formula relating Ext and Hom. [Copyright &y& Elsevier]

For a right artinian ring A we show that for every n ≥ 0 there exists a pure-injective A-module P[subn] such that the A-modules of projective dimension at most n are precisely the direct factors of A-modules having a finite filtration in products of copies of P[subn]. This is a consequence of a general description of certain contravariantly finite resolving subcategories of Mod A. It leads in addition to a one-to-one correspondence between equivalence classes of (not necessarily finitely generated) cotilting modules and resolving subcategories of Mod A which are closed under products and admit finite resolutions and special right approximations. As an application it is shown that every finitely presented partial cotilting module over an artin algebra admits a complement. [ABSTRACT FROM AUTHOR]

The notion of tameness for the derived category of a finite dimensional algebra is introduced and standard properties are established. This is based on classical tameness definitions of Drozd and Crawley-Boevey for the category of finite dimensional representations. [ABSTRACT FROM AUTHOR]

Let Λ and Γ be finite dimensional algebras. It is shown that any stable equivalence f:mod¯Λ→mod¯Γ between the categories of finitely generated modules induces a bijection M ↦ Mf between the sets of isomorphism classes of generic modules over Λ and Γ such that the endolength of Mf is bounded by the endolength of M up to a scalar which depends only on f. Using Crawley-Boevey's characterization of tame representation type in terms of generic modules, one obtains as a consequence a new proof for the fact that a stable equivalence preserves tameness. This proof also shows that polynomial growth is preserved. 2000 Mathematics Subject Classification 16G60, 16D90. [ABSTRACT FROM AUTHOR]