| FullText URL | mjou_063_153_165.pdf |
|---|---|
| Author | Seita, Kohei| |
| Abstract | Let G be a finite group and let V and W be real G-modules. We call V and W dim-equivalent if for each subgroup H of G, the H-fixed point sets of V and W have the same dimension. We call V and W are Smith equivalent if there is a smooth G-action on a homotopy sphere Σ with exactly two G-fixed points, say a and b, such that the tangential G-representations at a and b of Σ are respectively isomorphic to V and W . Moreover, We call V and W are d-Smith equivalent if they are dim-equivalent and Smith equivalent. The differences of d-Smith equivalent real G-modules make up a subset, called the d-Smith set, of the real representation ring RO(G). We call V and W P(G)-matched if they are isomorphic whenever the actions are restricted to subgroups with prime power order of G. Let N be a normal subgroup. For a subset F of G, we say that a real G-module is F-free if the H-fixed point set of the G-module is trivial for all elements H of F. We study the d-Smith set by means of the submodule of RO(G) consisting of the differences of dim-equivalent, P(G)-matched, {N}-free real G-modules. In particular, we give a rank formula for the submodule in order to see how the d-Smith set is large. |
| Keywords | Real G-module Smith equivalence representation ring Oliver group |
| Published Date | 2021-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume63 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 153 |
| End Page | 165 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©2021 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | Shitanda, Yoshimi| |
|---|---|
| Published Date | 2017-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume59 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/54712 |
| Author | Wakimoto, Kazumasa| |
|---|---|
| Published Date | 1974-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume17 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33910 |
| Author | Blanco-Ferro, Antonio A.| Lopez Lopez, Miguel A.| |
|---|---|
| Published Date | 1986-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume28 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33945 |
| Author | Kobayashi, Yuji| |
|---|---|
| Published Date | 1981-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume23 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33842 |
| Author | Nakajima, Atsushi| |
|---|---|
| Published Date | 1978-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume20 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33963 |
| FullText URL | mjou_061_159_166.pdf |
|---|---|
| Author | Tasaka, Fuminori| |
| Abstract | A 2-block of a finite group having a Klein four hyperfocal subgroup has the same number of irreducible Brauer characters as the corresponding 2-block of the normalizer of the hyperfocal subgroup. |
| Keywords | group theory modular representation hyperfocal subgroup |
| Published Date | 2019-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume61 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 159 |
| End Page | 166 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| language | English |
| Copyright Holders | Copyright©2019 by the Editorial Board of Mathematical Journal of Okayama University |
| Author | TRIMÈCHE, Khalifa| |
|---|---|
| Published Date | 2016-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume58 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/53925 |
| Author | Niederreiter, Harald| |
|---|---|
| Published Date | 1988-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume30 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33556 |
| Author | Ito, Noboru| |
|---|---|
| Published Date | 1984-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume26 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33339 |
| Author | Moriya, Mikao| |
|---|---|
| Published Date | 1955-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume5 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33572 |
| Author | Moriya, Mikao| |
|---|---|
| Published Date | 1953-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume2 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33167 |
| Author | Otsuki, Tominosuke| |
|---|---|
| Published Date | 1957-07 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume7 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33642 |
| Author | Otsuki, Tominosuke| |
|---|---|
| Published Date | 1957-12 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume7 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33636 |
| Author | Numakura, Katsumi| |
|---|---|
| Published Date | 1955-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume5 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33574 |
| Author | Numakura, Katsumi| |
|---|---|
| Published Date | 1956-03 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume5 |
| Issue | issue2 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33565 |
| Author | Otsuki, Tominosuke| |
|---|---|
| Published Date | 1954-10 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume4 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33755 |
| Author | Tasaka, Takashi| |
|---|---|
| Published Date | 1996-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume38 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33093 |
| Author | Tasaka, Takashi| |
|---|---|
| Published Date | 1994-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume36 |
| Issue | issue1 |
| Content Type | Journal Article |
| JaLCDOI | 10.18926/mjou/33206 |
| FullText URL | mjou_060_037_058.pdf |
|---|---|
| Author | Masuda, Toshihiko| |
| Abstract | We give a survey of Tomita-Takesaki theory and the development of analysis of structure of type III factors, which started from Tomita-Takesaki theory. |
| Keywords | Tomita-Takesaki theory type III factors injective factors |
| Published Date | 2018-01 |
| Publication Title | Mathematical Journal of Okayama University |
| Volume | volume60 |
| Issue | issue1 |
| Publisher | Department of Mathematics, Faculty of Science, Okayama University |
| Start Page | 37 |
| End Page | 58 |
| ISSN | 0030-1566 |
| NCID | AA00723502 |
| Content Type | Journal Article |
| Official Url | http://www.math.okayama-u.ac.jp/mjou/| |
| language | English |
| Copyright Holders | Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University |
