Introduction to group representations and characters
著者
書誌事項
Introduction to group representations and characters
（North-Holland mathematics studies, 175 . Group representations / Gregory Karpilovsky ; v. 1,
North-Holland, 1992
並立書誌 全1件
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Background material / Gregory Karpilovsky
BA18303684
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Background material / Gregory Karpilovsky
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注記
Includes bibliographical references (p. 1231-1254)
Includes index
内容説明・目次
内容説明
The principal object of this multi-volume treatise is to provide, in a self-contained manner, comprehensive coverage of the mainstream of group representation theory. The audience for these volumes consists of aspiring graduate students and mature mathematicians working in the field of group representations. No mathematical knowledge is presupposed beyond the rudiments of abstract algebra, set theory and field theory; however, a certain maturity in mathematical reasoning is required. Apart from a few obvious exceptions, the volumes are entirely self-contained. The style of the presentation is informal: the author is not afraid to repeat definitions and formulas when necessary. Many sections begin with a nontechnical description and special effort has been made to render the exposition transparent.
目次
Background Material. Rings and Modules. Artinian and Semilocal Rings. Homological Algebra. Restriction, Induction and Coinduction. Semiperfect Rings. Complexes, Homology and Resolutions. Heller Operators. Group Algebras. Group Cohomology. Graded Algebras and Crossed Products. Algebras over Fields. The Brauer Group. Indecomposable Modules and Ground Field Extensions. The Schur Index. Frobenius and Symmetric Algebras. Dedekind Domains and Discrete Valuation Rings. Introduction to Group Representations. Generalities. Induced Modules. Introduction to Characters. An Invitation to Characters. Induction Theorems and Applications. Central, Faithful and Permutation Characters. Character Tables. Zeros of Characters. Characters, Conjugate Elements and Commutators. The Frobenius-Schur Indicator. Characters and Hall Subgroups. Extensions of Characters. Irreducible Constituents and Conjugacy Classes. Fixed-Point Spaces and Powers of Characters. Determinants of Characters. Tensor Induction of Characters. Knorr's Generalized Character. Characters of Centralizer Rings. Characters and Relative Normal Complements. Isometries and Generalized Characters. Exceptional Characters. Frobenius Groups. Applications of Characters. Bibliography. Notation. Index.
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