Varieties of elementary abelian Lie algebras and degrees of modules,Representation Theory

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Varieties of elementary abelian Lie algebras and degrees of modules
Representation Theory ( IF 0.7 ) Pub Date : 2021-02-11 , DOI: 10.1090/ert/559
Hao Chang , Rolf Farnsteiner

Abstract:Let $(\mathfrak{g},[p])$ be a restricted Lie algebra over an algebraically closed field

of characteristic $p\!\ge \!3$ . Motivated by the behavior of geometric invariants of the so-called $(\mathfrak{g},[p])$ -modules of constant

-rank ( $j \in \{1,\ldots ,p\!-\!1\}$ ), we study the projective variety $\mathbb{E}(2,\mathfrak{g})$ of two-dimensional elementary abelian subalgebras. If $p\!\ge \!5$ , then the topological space $\mathbb{E}(2,\mathfrak{g}/C(\mathfrak{g}))$ , associated to the factor algebra of $\mathfrak{g}$ by its center $C(\mathfrak{g})$ , is shown to be connected. We give applications concerning categories of $(\mathfrak{g},[p])$ -modules of constant

-rank and certain invariants, called

-degrees.

中文翻译：

基本的阿贝尔李代数的种类和模的阶数

摘要：设特征为的代数封闭域上的受限李代数。受所谓的常数-rank（- ）的-模的几何不变性的影响，我们研究了二维基本阿贝尔亚代数的射影变体。如果为，则表示与其中心的因子代数关联的拓扑空间是连通的。我们给出有关常量-rank和某些不变式-modules的-modules类的应用程序。 $（\ mathfrak {g}，[p]）$

$p \！\ ge \！3$ $（\ mathfrak {g}，[p]）$

$j \ in \ {1，\ ldots，p \！-\！1 \}$ $\ mathbb {E}（2，\ mathfrak {g}）$ $p \！\ ge \！5$ $\ mathbb {E}（2，\ mathfrak {g} / C（\ mathfrak {g}））$ $\ mathfrak {g}$ $C（\ mathfrak {g}）$ $（\ mathfrak {g}，[p]）$

更新日期：2021-02-12

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