2017 Fiscal Year Final Research Report
Various aspecst of pseudo-reflection groups and related topics
| Project/Area Number |
26400019
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | J. F. Oberlin University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
ISHIBASI Hiroyuki 城西大学, 理学部, 名誉教授 (90118513)
YAMAGUCHI Hiroshi 城西大学, 理学部, 教授 (20137798)
SEKIGUCHI Katsusuke 国士舘大学, 理工学部, 教授 (20146749)
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Keywords | 擬鏡映 / 代数群 / コンパクト群 / クルル環 / 因子類群 / 非アフィン環 / 半不変式 / セリュラーオートマトン |
|---|
| Outline of Final Research Achievements |
Let G be an algebraic group with the identity component G0 over an algebraically closed field K of characteristic p. Denote by (R, G) an integral K-domain R with a regular action of G. In the case that G0 is a torus, we show a criterion for G to be a finite central extension of G0 in terms of ramification theory of all regular actions of any closed subgroup H containing the centralizer of G0 in G on Krull K-domains (R, H) satisfying the invariant quotient field condition on (R, H). Generally suppose G0 is reductive. Let T be a subtorus of G under the similar condition on quotient fields. We show: If G is the centralizer of T in G, then the pseudo-reflections of the action of G on the ring of invariants of T in R can be lifted to those on R.
Let G assumed to be connected and consider (R, G) with a Krull R. We give the minimal calculation of the ring S of invariants of G in R and their class groups by cutting the prime semi-invariants which form free modules over S.
|
| Free Research Field |
代数学
|
