2012 Fiscal Year Final Research Report
A study for the categorical representation theory for finite groups and algebra
Project/Area Number |
21540031
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Yamagata University |
Principal Investigator |
ODA Fumihito 山形大学, 理学部, 准教授 (00332007)
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Project Period (FY) |
2009 – 2012
|
Keywords | 有限群論 / 表現論 / カテゴリー論 / 圏論 |
Research Abstract |
(1) For a finite group and a certain family of subgroups of the group induce a categoryand a commutative ring. The ring is called generalized Burnside ring. So far only afew examples of such families of subgroups have been examined. We introduced anew family in the case when the coefficient ring is the localization of the rationalintegers at any prime. The family consists of normalizers of certain p-radical subgroups. We investigate the kernel of certain homomorphism and the units andprimitive idempotents of the ring. It is shown that the degree of the generalizedcharacter afforded by the multiplicative identity (unit) of the ring coincides withthe Euler characteristic of the order complex of the family of subgroups of the group. (2) By using a theorem of p-biset functor obtained by Bouc and Thevenaz, we have arelationship between the Dade group, crossed Burnside ring and rational representation ring of Drinfeld double for a p-group. (3) We described the construction of the crossed Burnside ring for a finite group via theDress construction applied to the Burnside Tambara functor.
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Research Products
(14 results)