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Group theory --- Eindige groepen --- Finite groups --- Groepen [Eindige ] --- Groupes finis --- Groups [Finite ] --- Representation des groupes --- Representations of groups --- Vertegenwoordiging van groepen --- Finite groups. --- Representations of groups.
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Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader ha
Ordered algebraic structures --- Group algebras. --- Jacobson radical. --- Modules (Algebra) --- Group algebras --- Jacobson radical --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Jacobson's radical --- Radical, Jacobson --- Radical theory --- Algebras, Group --- Abelian groups --- Locally compact groups
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In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings.The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and g
Ordered algebraic structures --- Von Neumann algebras --- C*-algebras. --- Crossed products. --- Crossed products --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Crossed products of Von Neumann algebras --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Von Neumann algebras - Crossed products
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Class field theory --- Corps de classe --- Groepentheorie --- Group theory --- Groupes [Théorie des ] --- Groups [Theory of ] --- Theory of groups --- Théorie des groupes
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512.55 --- Abelian groups --- Commutative algebra --- Group algebras --- Algebras, Group --- Locally compact groups --- Algebra --- Commutative groups --- Group theory --- Rings and modules --- 512.55 Rings and modules
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This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theo
Representations of groups. --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory
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In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each
Group algebras. --- Modules (Algebra) --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- Algebras, Group --- Abelian groups --- Locally compact groups --- Group algebras
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Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpos
Clifford algebras. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Geometric algebras --- Algebras, Linear
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A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.
Group rings --- Semigroup rings --- 512.55 --- 512.55 Rings and modules --- Rings and modules --- Rings, Semi group --- Rings, Semigroup --- Semi group rings --- Rings (Algebra) --- Semigroups --- Group theory --- Congresses
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