## Convexity in a masure. (arXiv:1710.09272v2 [math.GR] UPDATED)

Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.