Articoli correlati a Modular Representation Theory of Finite Groups
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This book provides a concise introduction to modular representation theory for masters-level students. It details basic results, tools, and techniques as well as compares group theoretic and module theoretic concepts.
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Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group.
Modular representation theory of finite groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field.
Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given.
This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.
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MODULAR REPRESENTATION THEORY OF FINITE GROUPS (PB 2018)
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Modular Representation Theory Of Finite Groups
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MODULAR REPRESENTATION THEORY OF FINITE GROUPS (PB 2018)
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MODULAR REPRESENTATION THEORY OF FINITE GROUPS (PB 2018)
Edizione InternazionaleDa: Romtrade Corp., STERLING HEIGHTS, MI, U.S.A.
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Condizione: New. Brand New. Soft Cover International Edition. Different ISBN and Cover Image. Priced lower than the standard editions which is usually intended to make them more affordable for students abroad. The core content of the book is generally the same as the standard edition. The country selling restrictions may be printed on the book but is no problem for the self-use. This Item maybe shipped from US or any other country as we have multiple locations worldwide. Codice articolo ABNR-53574
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Modular Representation Theory of Finite Groups
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Springer London Nov 2012, 2012
ISBN 10: 1447148312
ISBN 13: 9781447148319
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group.Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field.Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained. 188 pp. Englisch. Codice articolo 9781447148319
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Modular Representation Theory of Finite Groups
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Modular Representation Theory of Finite Groups
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Springer London, Springer London Nov 2012, 2012
ISBN 10: 1447148312
ISBN 13: 9781447148319
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Taschenbuch
Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germania
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Taschenbuch. Condizione: Neu. Neuware -Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for exampleover the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group.Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocksof the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field.Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given.This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) inthe text. Otherwise the book is entirely self-contained.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 188 pp. Englisch. Codice articolo 9781447148319
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Modular Representation Theory of Finite Groups
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