Solvability and nilpotency for algebraic supergroups
Solvability and nilpotency for algebraic supergroups
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DOI：
10.1016/j.jpaa.2016.06.012
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
A. Masuoka;A. Zubkov
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文献类型：
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作者：
A. Masuoka;A. Zubkov
本文研究了特征特征数为K <$2的域K上代数超群的可解性、幂零性和分裂性。我们的第一个主要定理告诉我们，一个代数超群G是可解的，如果相关的代数群G e v是可三角化的。为了证明这一点，我们确定了代数超群G，使得dim ∈ Lie（G）1= 1;当G ∈ v可对角化时，研究了它们的表示.第二个主要定理刻画了幂零连通代数超群。证明了Chevalley分解定理的一个超类似，尽管它必须是弱形式的。给出了光滑Noether超代数和光滑Hopf超代数的一个附录。
We study solvability, nilpotency and splitting property for algebraic supergroups over an arbitrary field K of characteristic char K≠ 2. Our first main theorem tells us that an algebraic supergroup G is solvable if the associated algebraic group G e v is trigonalizable. To prove it we determine the algebraic supergroups G such that dim Lie (G) 1= 1; their representations are studied when G e v is diagonalizable. The second main theorem characterizes nilpotent connected algebraic supergroups. A super-analogue of the Chevalley Decomposition Theorem is proved, though it must be in a weak form. An appendix is given to characterize smooth Noetherian superalgebras as well as smooth Hopf superalgebras.