By David J. Benson, Henning Krause, Andrzej Skowronski
ISBN-10: 3037191252
ISBN-13: 9783037191255
This quantity provides a suite of articles dedicated to representations of algebras and comparable subject matters. Dististinguished specialists during this box provided their paintings on the foreign convention on Representations of Algebras which happened 2012 in Bielefeld. the various expository surveys are integrated right here. Researchers of illustration thought will locate during this quantity attention-grabbing and stimulating contributions to the improvement of the topic.
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Cambridge Philos. Soc. 132 (2002), 89–96. [4] L. Angeleri Hügel, D. Herbera, and J. Trlifaj, Tilting modules and Gorenstein rings. Forum Math. 18 (2006), 217–235. [5] L. Angeleri Hügel, D. Herbera, and J. Trlifaj, Divisible modules and localization. J. Algebra 294 (2005), 519–551. [6] L. Angeleri Hügel, O. Kerner, and J. Trlifaj, Large tilting modules and representation type. Manuscr. Math. 132 (2010), 483–499. [7] L. Angeleri Hügel, S. Koenig, Q. Yang, Derived simple algebras and restrictions of recollements of derived module categories.
6]. 3 that TU is a tilting module with tilting class U? 8 Classification of tilting modules Now we are ready for the first classification results. 11] to prove that over certain hereditary rings all tilting modules are of the form TU for some set of simple modules U. g. not necessarily commutative discrete valuation domains), and to Dedekind domains. 1 Dedekind domains ([21], [11]). e. a commutative noetherian hereditary domain, for example R D Z. Every tilting module is equivalent to a module of the form TU where U is a set of simple R-modules.
The action of  is via m ˝ 1 7! , the action of  on the copy of M at ˛N 2 P r 1 is via X˛ . Notice that the twist is necessary in order to make this well defined on projective space. 6 (Benson and Pevtsova [6]). M / D Ker  \ Im  i 1 Ker  \ Im  i z. as subquotient of M Now Ker  picks out the socles of all Jordan blocks. Ker  \ Im  i picks out the socles of the Jordan blocks of length at least i C 1. So Fi is a subquotient which picks out the socles of the Jordan blocks of length i . 7. M / is a vector bundle for 1 Ä i Ä p if and only if M has constant Jordan type.
Advances in Representation Theory of Algebras by David J. Benson, Henning Krause, Andrzej Skowronski
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