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Moduli of representations and related topics (3)

Research Project

Project/Area Number 15K04814
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionUniversity of Yamanashi

Principal Investigator

NAKAMOTO Kazunori  山梨大学, 大学院総合研究部, 教授 (30342570)

Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords代数学 / 代数幾何学 / 不変式論 / 表現のモジュライ
Outline of Final Research Achievements

The paper on the construction of the moduli of representations of degree 2 for each mold has been published. We published the paper on topological properties of the moduli of representations with each mold of degree 2 for free monoids (joint work with Takeshi Torii(Okayama University)). We also published the paper on basic results on thick representations and dense representations, which are special types of irreducible representations (joint work with Yasuhiro Omoda(National Institute of Technology, Akashi College)). As a collaboration with Takeshi Torii, we see that we can apply Hochschild cohomology to the moduli of subalgebras of the full matrix ring. We calculated Hochschild cohomology for each subalgebra of the full matrix ring of degree 3. These results will be announced.

Academic Significance and Societal Importance of the Research Achievements

行列は基本的な代数的対象であり、複数個の行列を同時に分かりやすい標準型に変形することは、数学のさまざまな分野に多くの応用が考えられ有益である。群やモノイドといった代数的構造をもつ集合を行列に表現することは古くから考えられ、1つの表現(の同値類)を1点とするような幾何学的対象(表現のモジュライ)を調べることが本研究のテーマである。行列環の部分代数Aに対して、像が生成する部分代数がAに一致するような表現を集めると、Aに対する表現のモジュライが作られるであろうと予想し、実際に構成するのが本研究の目的である。今回、2次の表現のモジュライや3次の行列環の部分代数のモジュライに関する豊富な結果が得られた。

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (23 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (5 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 5 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) Remarks (5 results)

  • [Int'l Joint Research] Galatasaray University(トルコ)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] University of Rhode Island(米国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Thick representations and dense representations I2019

    • Author(s)
      Nakamoto Kazunori and Omoda Yasuhiro
    • Journal Title

      Kodai Mathematical Journal

      Volume: 42 Issue: 2 Pages: 274-307

    • DOI

      10.2996/kmj/1562032831

    • NAID

      130007674785

    • ISSN
      0386-5991, 1881-5472
    • Year and Date
      2019-06-27
    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on kernel Bayes’ rule2018

    • Author(s)
      Johno Hisashi、Nakamoto Kazunori、Saigo Tatsuhiko
    • Journal Title

      Cogent Mathematics & Statistics

      Volume: 5 Issue: 1 Pages: 1447220-1447220

    • DOI

      10.1080/23311835.2018.1447220

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Triple root systems, rational quivers and examples of linear free divisors2018

    • Author(s)
      Kazunori Nakamoto, Ayse Sharland, and Meral Tosun
    • Journal Title

      International Journal of Mathematics

      Volume: 29 Issue: 03 Pages: 1850017-1850017

    • DOI

      10.1142/s0129167x18500179

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The moduli of representations of degree 22017

    • Author(s)
      Kazunori Nakamoto
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 57 Issue: 4 Pages: 829-902

    • DOI

      10.1215/21562261-2017-0017

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Virtual Hodge polynomials of the moduli spaces of representations of degree 2 for free monoids2016

    • Author(s)
      Kazunori Nakamoto and Takeshi Torii
    • Journal Title

      Kodai Mathematical Journal

      Volume: 39 Issue: 1 Pages: 80-109

    • DOI

      10.2996/kmj/1458651693

    • NAID

      130005475880

    • ISSN
      0386-5991, 1881-5472
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] An application of Hochschild cohomology to the moduli of subalgebras of the full matrix ring II2019

    • Author(s)
      鳥居猛、中本和典
    • Organizer
      第8回日中韓環論国際シンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] An application of Hochschild cohomology to the moduli of subalgebras of the full matrix ring II2019

    • Author(s)
      鳥居猛、中本和典
    • Organizer
      日本数学会代数学分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Hochschild cohomologyの計算例と行列環の部分代数のモジュライへの応用2019

    • Author(s)
      中本 和典
    • Organizer
      第47回神楽坂代数セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] The moduli of 4-dimensional subalgebras of M_32019

    • Author(s)
      中本 和典
    • Organizer
      「非可換代数幾何学の大域的問題とその周辺」高知小研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] An application of the moduli of subalgebras of the full matrix ring2018

    • Author(s)
      鳥居猛,中本和典
    • Organizer
      第51回環論および表現論シンポジウム
    • Related Report
      2018 Research-status Report
  • [Presentation] 3次行列環の部分代数のモジュライ(2)2018

    • Author(s)
      鳥居猛,中本和典
    • Organizer
      日本数学会代数学分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] An application of the moduli of subalgebras of the full matrix ring2018

    • Author(s)
      鳥居猛,中本和典
    • Organizer
      日本数学会代数学分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] 3次行列環の部分代数のモジュライ(1)2017

    • Author(s)
      鳥居猛、中本和典
    • Organizer
      日本数学会2017年度年会代数学分科会
    • Place of Presentation
      首都大学東京南大沢キャンパス(東京都八王子市南大沢)
    • Year and Date
      2017-03-26
    • Related Report
      2016 Research-status Report
  • [Presentation] The moduli of subalgebras of the full matrix ring of degree 32017

    • Author(s)
      Kazunori Nakamoto and Takeshi Torii
    • Organizer
      第50回環論および表現論シンポジューム
    • Related Report
      2017 Research-status Report
  • [Presentation] Two-dimensional traceless representations in characteristic 22016

    • Author(s)
      中本和典
    • Organizer
      日本数学会2016年度秋季総合分科会代数学分科会
    • Place of Presentation
      関西大学千里山キャンパス(大阪府吹田市山手町)
    • Year and Date
      2016-09-18
    • Related Report
      2016 Research-status Report
  • [Presentation] 決定木を用いた確率分布間のoverlap の計算2016

    • Author(s)
      城野悠志、中本和典
    • Organizer
      日本数学会2016年度秋季総合分科会統計数学分科会
    • Place of Presentation
      関西大学千里山キャンパス(大阪府吹田市山手町)
    • Year and Date
      2016-09-17
    • Related Report
      2016 Research-status Report
  • [Remarks] 山梨大学 教員情報検索

    • URL

      http://nerdb-re.yamanashi.ac.jp/Profiles/322/0032156/profile.html

    • Related Report
      2019 Annual Research Report 2018 Research-status Report 2017 Research-status Report 2016 Research-status Report
  • [Remarks] 山梨大学医学部総合医科学センター[数学]

    • URL

      https://www.med.yamanashi.ac.jp/medicine/mathematics/

    • Related Report
      2019 Annual Research Report
  • [Remarks] 山梨大学医学部医学教育センター[数学]

    • URL

      https://www.med.yamanashi.ac.jp/medicine/mathematics/

    • Related Report
      2018 Research-status Report 2017 Research-status Report
  • [Remarks] 山梨大学医学部医学教育センター[数学]

    • URL

      http://www.med.yamanashi.ac.jp/medicine/mathematics/index.html

    • Related Report
      2016 Research-status Report 2015 Research-status Report
  • [Remarks] 山梨大学 研究者総覧 研究者公開情報

    • URL

      http://sangaku.yamanashi.ac.jp/SearchResearcher/contents/D064338FEDDFC538.html

    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2022-02-21  

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