Categorical study of representation theory of finite groups and algebras

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400003
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kinki University
• Principal Investigator: ODA Fumihito 近畿大学, 理工学部, 准教授 (00332007)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: バイセット関手 / バーンサイド環 / 一般バーンサイド環 / 対称群 / 二面体群 / 単元群

Outline of Final Research Achievements

We showed that there is a relation between the unit element of the generalized Burnside ring of a symmetric group relative to the Young subgroups, the reduced Lefschetz module and the tom Dieck homomorphism. More precisely, we characterized a non-identity unit of the generalized Burnside ring of a symmetric group relative to the Young subgroups in terms of the tom Dieck homomorphism. Consequently, we have shown that the unit group of the ring is included in the image by the tom Dieck homomorphism. We have submitted to a paper of the result to a journal of mathematics.
We showed that the rank of the unit group of the generalized Burnside ring of a dihedral group relative to the parabolic subgroups is two. We have submitted to a paper of the result to a journal of mathematics.

Free Research Field

有限群の表現論