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Transformation semigroups associated to Γ-semigroups

Dariush Heidari, Marzieh Amooshahi (2013)

Discussiones Mathematicae - General Algebra and Applications

The concept of Γ-semigroups is a generalization of semigroups. In this paper, we associate two transformation semigroups to a Γ-semigroup and we call them the left and right transformation semigroups. We prove some relationships between the ideals of a Γ-semigroup and the ideals of its left and right transformation semigroups. Finally, we study some relationships between Green's equivalence relations of a Γ-semigroup and its left (right) transformation semigroup.

Transience of algebraic varieties in linear groups - applications to generic Zariski density

Richard Aoun (2013)

Annales de l’institut Fourier

We study the transience of algebraic varieties in linear groups. In particular, we show that a “non elementary” random walk in S L 2 ( ℝ ) escapes exponentially fast from every proper algebraic subvariety. We also treat the case where the random walk takes place in the real points of a semisimple split algebraic group and show such a result for a wide family of random walks.As an application, we prove that generic subgroups (in some sense) of linear groups are Zariski dense.

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