2020 Fiscal Year Final Research Report
Super-groups and super-geometry from Hopf-algebraic view-point
| Project/Area Number |
17K05189
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
MASUOKA AKIRA 筑波大学, 数理物質系, 教授 (50229366)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | スーパー・ホップ代数 / スーパー代数群 / スーパー・リー群 |
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| Outline of Final Research Achievements |
Seven papers were published from international scientific journals, two of which resulted from international joint research. There were presented three lectures, which include one invited lecture at an international conference.
Obtained were fundamental results on algebraic supergroups and super Lie groups. Hopf-algebraic idea and techniques were applied. Among others, the PI concretely constructed the quotient superscheme G/H of an algebraic supergroup G by a closed super-subgroup H, and showed desirable properties of the superscheme; the result contributes much to representation theory of algebraic supergroups. Pursuing an analytic analogue of the algebraic argument brought some new results on homogeneous superspaces G/H of super Lie groups.
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| Free Research Field |
代数学
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| Academic Significance and Societal Importance of the Research Achievements |
スーパー幾何学は、スーパー・ストリング理論のインパクトから再び興味を呼んでいる研究分野ではあるが、一般論が十分整備されているとは言えず、膨大な数の文献の中には信頼できないものも多い。研究代表者は、この状況を打開する目的で、ホップ代数のアイデアとテクニックを応用して、当該一般論を展開する基本的方法を提示した。それは、通常の（非スーパー）コンテクストにおける議論を踏襲・一般化するのではなく、それに帰着させる方法であって、目的はある程度達成できたと思う。
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