| 000 | 02305cam a22002777a 4500 | ||
|---|---|---|---|
| 001 | 17529809 | ||
| 005 | 20250611104916.0 | ||
| 008 | 121115s2013 ne a b 001 0 eng d | ||
| 020 | _a9781447148319 | ||
| 040 |
_aCSL _cCSL |
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| 041 |
_2eng _aeng |
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| 084 |
_aB271 Q3 NBHM _qCSL |
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| 100 | 1 |
_aSchneider, P. _eauthor. _9812557 |
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| 245 | 1 | 0 | _aModular representation theory of finite groups |
| 260 |
_aDordrecht : _bSpringer, _c2013. |
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| 300 |
_aviii, 178 p. : _bill. ; _c24 cm. |
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| 504 | _aIncludes bibliographical references (p. 175) and index. | ||
| 505 | 0 | _a1. Prerequisites in module theory -- 2. The Cartan-Brauer Triangle -- 3. The Brauer character -- 4. Green's theory of indecomposable modules -- 5. Blocks. | |
| 520 | _aModular 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. | ||
| 650 | 0 |
_aModular representations of groups. _9812147 |
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| 650 | 0 |
_aBrauer Correspondence _9812558 |
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| 650 | 0 |
_aBurnside Ring _9812559 |
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| 650 | 0 |
_aFinite groups. _9439386 |
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| 650 | 0 |
_aCartan-Brauer Triangle _9812560 |
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| 942 |
_2CC _n0 _cTEXL _hB271 Q3 NBHM |
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| 999 |
_c1431593 _d1431593 |
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