KINDAI UNIVERSITY


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ODA Fumihito

Profile

FacultyDepartment of Science / Graduate School of Science and Engineering Research
PositionProfessor
Degree
Commentator Guidehttps://www.kindai.ac.jp/meikan/518-oda-fumihito.html
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Last Updated :2020/04/03

Education and Career

Education

  •   1986 04  - 1990 03 , Hokkaido University of Education
  •   1992 04  - 1997 09 , Kumamoto University, Graduate School of Science and Technology

Academic & Professional Experience

  •   2019 04 ,  - 現在, Professor, Faculty of Science and Technology, Kindai University
  •   2013 04 ,  - 2019 03 , Associate Professor, Faculty of Science and Technology, Kindai University
  •   2009 04 ,  - 2013 03 , Associate Professor, Faculty of Sciences, Yamagata university
  •   2009 04 ,  - 2013 03 , Faculty of Science, Yamagata University
  •   2008 04 ,  - 2009 03 , Associate Professor, Toyama National College of Maritime Technology
  •   2000 04 ,  - 2008 03 , Associate Professor, Toyama National College of Technology

Research Activities

Research Areas

  • Natural sciences, Algebra

Research Interests

  • unit group, crossed Burnside ring, Green functor, quantum double, GBR, Drinfeld double, algebra, Mackey, centric p-radical subgroup, category, Burnside, representation, finite group

Published Papers

  • The unit group of a partial Burnside ring of a reducible Coxeter group of type A, Fumihito Oda, Masahiro Wakatake, Hokkaido Mathematical Journal, Hokkaido Mathematical Journal, 48(2), 345 - 356, Jul. 2019 , Refereed
  • Categorical constructions related to finite groups, FUMIHITO ODA AND, HIROYUKI, NAKAOKA, Sugaku Expositions, Sugaku Expositions, 32(1), 57 - 86, Jun. 2019 , Refereed
  • Lefschetz invariants and Young characters for representations of the hyperoctahedral groups, F. Oda, Y. Takegahara, T. Yoshida, Journal of Algebra, Journal of Algebra, 512, 1 - 19, Oct. 2018 , Refereed
  • Axiomatic theory of Burnside rings. (I), Tomoyuki Yoshida, Fumihito Oda, Yugen Takegahara, Journal of Algebra, Journal of Algebra, 505, 339 - 382, Jul. 2018 , Refereed
  • The units of a partial Burnside ring relative to the Young subgroups of a symmetric group, Fumihito Oda, Yugen Takegahara, Tomoyuki Yoshida, Journal of Algebra, Journal of Algebra, 460, 370 - 379, Aug. 2016 , Refereed
  • The table of marks, the Kostka matrix, and the character table of the symmetric group, Idei, Hokuto, Oda, Fumihito, Journal of Algebra, Journal of Algebra, 429(1), 318 - 323, May 2015 , Refereed
  • On categorical constructions related to finite groups, Oda, Fumihito, Nakaoka, Hiroyuki, Sugaku, Sugaku, 67(1), 55 - 81, Jan. 2015 , Refereed
  • The generalized Burnside rings with respect to a collection of self-normalizing subgroups, Oda, Fumihito, Sawabe, Masato, Journal of Algebra, Journal of Algebra, 334(1), 219 - 231, May 2011 , Refereed
  • The crossed Burnside rings III: The Dress construction for a Tambara functor, Oda, Fumihito, Yoshida, Tomoyuki, Journal of Algebra, Journal of Algebra, 327(1), 31 - 49, Feb. 2011
  • The crossed Burnside ring, the Drinfel'd double, and the Dade group of a p-group, ODA F, Algebras and Representation Theory, Algebras and Representation Theory, 13(2), 231 - 242, Apr. 2010 , Refereed
  • A collection of subgroups for the generalized Burnside ring, Oda, Fumihito, Sawabe, Masato, Advances in Mathematics, Advances in Mathematics, 222(1), 307 - 317, Sep. 2009 , Refereed
  • The generalized Burnside ring with respect to p-centric subgroups, Oda F, Journal of Algebra, Journal of Algebra, 320(10), 3726 - 3732, Nov. 2008 , Refereed
  • Crossed Burnside rings and Bouc's construction of Green functors, ODA F, Journal of Algebra, Journal of Algebra, 315(1), 18 - 30, Sep. 2007 , Refereed
  • Crossed Burnside rings II : The Dress construction of a Green functor, Oda, Fumihito, Yoshida, Tomoyuki, Journal of Algebra, Journal of Algebra, 282(1), 58 - 82, Dec. 2004 , Refereed
  • Crossed Burnside rings. I. The fundamental theorem., F. Oda, T. Yoshida, J. Algebra, J. Algebra, 236(1), 29 - 79, 2001 , Refereed
  • On the generalized Burnside ring with respect to the Young subgroups of the symmetric group, Oda, Fumihito, Yoshida, Tomoyuki, Journal of Algebra, Journal of Algebra, 236(1), 349 - 354, 2001 , Refereed
  • Primitive idempotents of the Grothendieck ring of Mackey functors, oda fumihito, Hokkaido Math. J., Hokkaido Math. J., 27(2), 383 - 392, 1998 , Refereed
  • On defect groups of the Mackey algebras for finite groups, oda fumihito, Hokkaido Math. J., Hokkaido Math. J., 26(2), 405 - 409, 1997 , Refereed
  • A note on the decomposition of the Burnside rings of finite groups, oda fumihito, Hokkaido Math. J., Hokkaido Math. J., 25(1), 93 - 96, 1996 , Refereed

Misc

  • The table of marks, the Kostka matrix, and the character table of the symmetric group, oda fumihito, 1965, 1, 4,   2015 10
  • The units of a partial Burnside ring relative to the Young subgroups of a symmetric group,, oda fumihito, 66, 71,   2015
  • On multiplicative induction, oda fumihito, 1872, 151, 157,   2014 01
  • An Introduction to an Application of the Theory of G-sets, MATSUDA Shigeo, ODA Fumihito, 15, 1, 135, 138,   2008 08 25 , http://ci.nii.ac.jp/naid/110008445242
  • A morphism of Green functors (Cohomology Theory of Finite Groups and Related Topics), Oda Fumihito, RIMS Kokyuroku, 1581, 126, 134,   2008 02 , http://ci.nii.ac.jp/naid/110006622018
  • ON THE CROSSED BURNSIDE RINGS(Group Theory and Related Topics), ODA FUMIHITO, RIMS Kokyuroku, 1564, 14, 16,   2007 07 , http://ci.nii.ac.jp/naid/110006313705
  • Green functors and Bouc's construction (Algebraic Combinatorics), Oda Fumihito, RIMS Kokyuroku, 1440, 121, 124,   2005 07 , http://ci.nii.ac.jp/naid/110001257080
  • Crossed Burnside ring functor for S_3, ODA Fumihito, Bulletin of Toyama Technical College, 37, 53, 54,   2003 03 , http://ci.nii.ac.jp/naid/110000290842
  • Crossed Burnside ring of C_2, ODA Fumihito, Bulletin of Toyama Technical College, 36, 41, 45,   2002 03 , http://ci.nii.ac.jp/naid/110000290825
  • The Loewy and socle layers of the Burnside functor for a cyclicp-group, ODA Fumihito, Bulletin of Toyama Technical College, 35, 65, 68,   2001 03 , http://ci.nii.ac.jp/naid/110000290814
  • On cohomological Mackey functors (Cohomology theory of finite groups), Oda Fumihito, RIMS Kokyuroku, 1140, 107, 121,   2000 04 , http://ci.nii.ac.jp/naid/110000164255
  • On Burnside functors (Algebraic Combinatorics), Oda Fumihito, RIMS Kokyuroku, 1109, 118, 128,   1999 08 , http://ci.nii.ac.jp/naid/110000163740
  • Primitive idempotens of the Grothendieck ring of Mackey functors(Groups and Combinatorics), ODA FUMIHITO, RIMS Kokyuroku, 991, 53, 60,   1997 05 , http://ci.nii.ac.jp/naid/110004077172

Research Grants & Projects

  • Ministry of Education, Culture, Sports, Science and Technology, Grants-in-Aid for Scientific Research(基盤研究(C)), A study for the categorical representation theory for finite groups and algebra, (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.
  • Ministry of Education, Culture, Sports, Science and Technology, Grants-in-Aid for Scientific Research(基盤研究(C)), A study for the categorical representation theory for finite groups and algebras