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Various aspecst of pseudo-reflection groups and related topics

Research Project

Project/Area Number 26400019
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionJ. F. Oberlin University

Principal Investigator

Nakajima Haruhisa  桜美林大学, 自然科学系, 教授 (90145657)

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
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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 / 擬鏡映群 / 群作用 / Krullスキーム / 因子類 / 不変部分環 / 配置空間 / オートマトン / Krull整域 / 代数的トーラス / 因子 / 自由標数 / 不変式 / 正規代数多様体
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.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (16 results)

All 2018 2017 2016 2014 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (5 results) (of which Int'l Joint Research: 3 results) Remarks (4 results)

  • [Journal Article] Valuative characterization of central extensions of algebraic tori on Krull domains2018

    • Author(s)
      Haruhisa Nakajima
    • Journal Title

      JP Journal of Algebra, Number Theory and Applications

      Volume: 40 Issue: 2 Pages: 113-146

    • DOI

      10.17654/nt040020113

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Calculation of invariant subrings and their divisor class groups by cutting semi-invariants2018

    • Author(s)
      Haruhisa Nakajima
    • Journal Title

      RIMS Kokyuroku

      Volume: to appear

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Injectivity of cellular automata2018

    • Author(s)
      Hiroyuki Ishibashi
    • Journal Title

      J.P.Journal of Algebra, Number Theory and Applications

      Volume: 40 Issue: 2 Pages: 199-205

    • DOI

      10.17654/nt040020199

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Injectivity of global maps of cellular automata2018

    • Author(s)
      Hiroyuki Ishibashi
    • Journal Title

      J.P.Journal of Algebra, Number Theory and Applications

      Volume: to appear

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Product of discrete topological spaces2018

    • Author(s)
      Hiroyuki Ishibashi
    • Journal Title

      RIMS Kokyuroku

      Volume: to appear

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Measures of analytic type and semicharacters2018

    • Author(s)
      Hiroshi Yamaguchi
    • Journal Title

      Josai Mathematical Monographs

      Volume: 11 Pages: 27-35

    • NAID

      120006487231

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-invariance of measures of analytic type on locally compact abelian groups2014

    • Author(s)
      山口 博
    • Journal Title

      Hokkaido Mathematical Journal

      Volume: 43 Pages: 51-64

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] Calculation of invariant rings by cutting semi-invarians2018

    • Author(s)
      Haruhisa Nakajima
    • Organizer
      RIMS Symposia (open) "Developments of Language, Logic, Algebraic System and Computer Science"
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Product of Discrete topological spaces2018

    • Author(s)
      Hiroyuki Ishibashi
    • Organizer
      RIMS Symposia (open) "Developments of Language, Logic, Algebraic System and Computer Science"
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Liftings of pseudo-reflection groups on invariant subrings of Krull domains of algebraic subtori under actions of reductive groups2017

    • Author(s)
      Haruhisa Nakajima
    • Organizer
      日本数学会
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 解析的測度とsemicharacterについて2017

    • Author(s)
      Hiroshi Yamaguchi
    • Organizer
      JMM Workshop on Applied Functional Analysis
    • Related Report
      2017 Annual Research Report
  • [Presentation] Pseudo-reflections of stable regular actions of finite central extensions of algebraic tori in free characteristics2016

    • Author(s)
      Haruhisa Nakajima
    • Organizer
      The Mathematical Society of Japan
    • Place of Presentation
      関西大学
    • Related Report
      2016 Research-status Report
  • [Remarks] 代数学研究室(中島晴久)

    • URL

      http://www2.obirin.ac.jp/nakajima/senkou.htm

    • Related Report
      2017 Annual Research Report
  • [Remarks] 代数学研究室 中島晴久

    • URL

      http://www2.obirin.ac.jp/nakajima/senkou.htm

    • Related Report
      2016 Research-status Report
  • [Remarks] 代数学研究室

    • URL

      http://www2.obirin.ac.jp/nakajima/senkou.htm

    • Related Report
      2015 Research-status Report
  • [Remarks] 代数学研究室(中島 晴久)

    • URL

      http://www2.obirin.ac.jp/nakajima/senkou.htm

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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