By David J. Benson, Henning Krause, Andrzej Skowronski

ISBN-10: 3037191252

ISBN-13: 9783037191255

This quantity offers a set of articles dedicated to representations of algebras and comparable subject matters. Dististinguished specialists during this box provided their paintings on the overseas convention on Representations of Algebras which came about 2012 in Bielefeld. some of the expository surveys are incorporated right here. Researchers of illustration thought will locate during this quantity attention-grabbing and stimulating contributions to the advance of the topic.

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A survey of modules of constant Jordan type and vector bundles on projective space David J. Benson 1 Modules of constant Jordan type We begin with a little background on modular representation theory to put these lectures in context. Let G be a finite group and k be a field. A representation of G is a group homomorphism G ! n; k/ for some n, or equivalently a finitely generated kGmodule, where kG is the group algebra. A representation is reducible if after a change of basis the matrices have the form 0 .

Math. 58 (2006), 180–224. [80] C. M. Ringel, Infinite dimensional representations of finite dimensional hereditary algebras. Symposia Math. XXIII (1979), 321–412. [81] L. Salce, Cotorsion theories for abelian groups. Symposia Math. XXIII (1979), 11–32. [82] L. Salce, F -divisible modules and tilting modules over Prüfer domains. J. Pure Appl. Algebra 199 (2005), 245–259. Infinite dimensional tilting theory 37 [83] M. Saorín and J. Št’ovíˇcek, On exact categories and applications to triangulated adjoints and model structures.

3 Commutative noetherian rings. T ; F / in Mod-R (or more generally, in a Grothendieck category A) is hereditary if T is closed under subobjects. Let now R be a commutative noetherian ring. We are going to see that the cotilting torsion pairs over R are precisely the faithful hereditary torsion pairs in Mod-R, and they are parametrized in terms of certain sets of prime ideals. R/ we have q 2 P whenever q Ã p. R/ j p Ã I g is contained in P . For details on Gabriel topologies we refer to [89]. Here we just recall that the Gabriel topologies on R correspond bijectively to the hereditary torsion pairs in Mod-R.

### Advances in Representation Theory of Algebras by David J. Benson, Henning Krause, Andrzej Skowronski

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