Modular representation theory for blocks with cyclic defect groups via the Auslander-Reiten quiver
نویسندگان
چکیده
منابع مشابه
Modular Representation Theory of Blocks with Trivial Intersection Defect Groups
We show that Uno’s refinement of the projective conjecture of Dade holds for every block whose defect groups intersect trivially modulo the maximal normal p-subgroup. This corresponds to the block having p-local rank one as defined by Jianbei An and Eaton. An immediate consequence is that Dade’s projective conjecture, Robinson’s conjecture, Alperin’s weight conjecture, the Isaacs– Navarro conje...
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Recall that an algebraic module is aKG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander–Re...
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Traditionally, to study a root system R one starts by choosing a set of simple roots Π ⊂ R (or equivalently, polarization of the root system into positive and negative parts) which is then used in all constructions and proofs. To prove that the resulting answers are independent of the choice of simple roots, one uses the fact that any two choices of simple roots are conjugate under the action o...
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We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’s representability theorem. In a fundamental article [3], Auslander and Reiten introduced almost split sequences for the category of finitely generated modules over an artin algebra. These are short exact sequences which look almost like split exact sequences, but many authors prefer to call them Auslander...
متن کاملAuslander-Reiten theory revisited
We recall several results in Auslander-Reiten theory for finite-dimensional algebras over fields and orders over complete local rings. Then we introduce n-cluster tilting subcategories and higher theory of almost split sequences and Auslander algebras there. Several examples are explained. Mathematics Subject Classification (2000). Primary 16G70; Secondary 16E30, 16G30.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1991
ISSN: 0021-8693
DOI: 10.1016/0021-8693(91)90155-2