Infinitely transitive actions on real affine suspensions

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• 作者：Karine Kuyumzhiyan^a ; ^b ; ^c ; ^{karina@mccme.ru} ; Fré ; dé ; ric Mangolte^d ; ^{Frederic.Mangolte@univ-angers.fr}
• 关键词：14R20 ; 14P99
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2012
• 期刊代码：35_00224049
• 类别：mt
• 出版时间：October, 2012
• 卷：216
• 期：10
• 页码：2106-2112
• 文件大小：234 K

摘要

A group acts infinitely transitively on a set if for every positive integer , its action is -transitive on . Given a real affine algebraic variety of dimension greater than or equal to , we show that, under a mild restriction, if the special automorphism group of (the group generated by one-parameter unipotent subgroups) is infinitely transitive on each connected component of the smooth locus , then for any real affine suspension聽 over , the special automorphism group of is infinitely transitive on each connected component of . This generalizes a recent result given by Arzhantsev, Kuyumzhiyan, and Zaidenberg over the field of real numbers.