Displaying similar documents to “On the intersection of invariant rings.”

Relative property (T) and linear groups

Talia Fernós (2006)

Annales de l’institut Fourier

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Relative property (T) has recently been used to show the existence of a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs with relative property (T) available through the literature. This motivated the following result: A finitely generated group Γ admits a special linear representation with non-amenable R -Zariski closure if and only if it acts on an Abelian...

On symmetric semialgebraic sets and orbit spaces

Ludwig Bröcker (1998)

Banach Center Publications

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For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.

The Mordell–Lang question for endomorphisms of semiabelian varieties

Dragos Ghioca, Thomas Tucker, Michael E. Zieve (2011)

Journal de Théorie des Nombres de Bordeaux

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The Mordell–Lang conjecture describes the intersection of a finitely generated subgroup with a closed subvariety of a semiabelian variety. Equivalently, this conjecture describes the intersection of closed subvarieties with the set of images of the origin under a finitely generated semigroup of translations. We study the analogous question in which the translations are replaced by algebraic group endomorphisms (and the origin is replaced by another point). We show that the conclusion...

On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

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We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence ( G n ) of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank  ω n .