Cohomology of finite groups and homotopy theory of classifying space from the view point of representation theory

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540007
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Saitama University
• Principal Investigator: HIDA Akihiko 埼玉大学, 教育学部, 教授 (50272274)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 有限群 / コホモロジー / 分類空間 / Burnside 環 / 表現論

Outline of Final Research Achievements

The double Burnside algebra of a finite group is the algebra with basis corresponding to finite sets such that the group acts from both sides. This algebra contains the information on the splitting of classifying space of finite group in the stable homotopy category. We studied the stable splitting of classifying space of finite groups through the action of double Burnside algebra on the cohomology.
We mainly consider the nonabelian p-group of order p cubed and exponent p. We determined the multiplicity of summands in the stable splitting and cohomology of these summands with coefficient the field of p elements. Moreover, we obtain information on finite groups having this group as a Sylow p-subgroup.

Free Research Field

有限群の表現論