Detecting nilpotence and projectivity over finite unipotent supergroup schemes
| العنوان: | Detecting nilpotence and projectivity over finite unipotent supergroup schemes |
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| المؤلفون: | Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar |
| المصدر: | Selecta Mathematica. 27 |
| بيانات النشر: | Springer Science and Business Media LLC, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Finite group, Pure mathematics, Steenrod algebra, General Mathematics, Mathematics::Rings and Algebras, 010102 general mathematics, General Physics and Astronomy, Field (mathematics), Unipotent, 01 natural sciences, Cohomology, Nilpotent, FOS: Mathematics, Perfect field, 16G10 (primary), 20C20, 20G10, 20J06 (secondary), Representation Theory (math.RT), 0101 mathematics, Mathematics::Representation Theory, Supergroup, Mathematics - Representation Theory, Mathematics |
| الوصف: | This work concerns the representation theory and cohomology of a finite unipotent supergroup scheme $G$ over a perfect field $k$ of positive characteristic $p\ge 3$. It is proved that an element $x$ in the cohomology of $G$ is nilpotent if and only if for every extension field $K$ of $k$ and every elementary sub-supergroup scheme $E\subseteq G_K$, the restriction of $x_K$ to $E$ is nilpotent. It is also shown that a $kG$-module $M$ is projective if and only if for every extension field $K$ of $k$ and every elementary sub-supergroup scheme $E\subseteq G_K$, the restriction of $M_K$ to $E$ is projective. The statements are motivated by, and are analogues of, similar results for finite groups and finite group schemes, but the structure of elementary supergroups schemes necessary for detection is more complicated than in either of these cases. One application is a detection theorem for the nilpotence of cohomology, and projectivity of modules, over finite dimensional Hopf subalgebras of the Steenrod algebra. 46 pages; Sections 12 on Z-graded group schemes and the Steenrod algebra is revised compared to the previous version |
| تدمد: | 1420-9020 1022-1824 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::219bc421b8e46d29c56a66c133afd86f https://doi.org/10.1007/s00029-021-00632-7 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....219bc421b8e46d29c56a66c133afd86f |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 14209020 10221824 |
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