（2k + 1）-分次李代数的广义旗几何
Generalized flag geometries associated with (2k + 1)-graded Lie algebras
摘要：
本文构造了一个与（2k +1）-分次李代数$g=g_k\oplus\dots\oplus g_{-k}$对应的几何对象，称为广义旗几何$(X^+;X^-)$.本文利用“双有理“映射证明了$(X^+;X^-) can be realized inside the space of inner filtrations of g and we use this realization to construct "algebraic bundles" on $ X^+ $ and $ X^- $ and some sections of these bundles. Thanks to these constructions, we can give a realization of $ g $ as a Lie algebra of polynomial maps on the positive part of $ g $, $ n^+_1：=g_1 \oplus \dots \oplus g_k $, and a trivialization in $ n^+_1 $ of the action of the group of automorphisms of $ g$.
英文摘要：
In this paper, we present the construction of a geometric object, called a generalized flag geometry, $(X^+;X^-)$, corresponding to a (2k +1)-graded Lie algebra $g=g_k\oplus\dots\oplus g_{-k}$. We prove that $(X^+;X^-) can be realized inside the space of inner filtrations of g and we use this realization to construct "algebraic bundles" on $X^+$ and $X^-$ and some sections of these bundles. Thanks to these constructions, we can give a realization of $g$ as a Lie algebra of polynomial maps on the positive part of $g$, $n^+_1:=g_1\oplus\dots\oplus g_k$, and a trivialization in $n^+_1$ of the action of the group of automorphisms of $g$ by "birational"maps.
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