Infinitely transitive actions on real affine suspensions

Karine Kuyumzhiyan; Frédéric Mangolte

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arXiv · 1012.1961

Infinitely transitive actions on real affine suspensions

Karine Kuyumzhiyan·Frédéric Mangolte

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Abstract

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

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Karine Kuyumzhiyan, Frédéric Mangolte. 2010-12-09. Infinitely transitive actions on real affine suspensions. https://arxiv.org/abs/1012.1961

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