5 papers
Picard Groups Of Algebraic Groups And An Affineness Criterion
Zev Rosengarten
We prove that an algebraic group over a field is affine precisely when its Picard group is torsion, and show that in this case the Picard group is finite when is perfect, an…
Quasi-connected reductive groups
Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten
We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth grou…
Galois cohomology of real quasi-connected reductive groups
Mikhail Borovoi, Andrei A. Gornitskii, Zev Rosengarten
By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group…
Translation-Invariant Line Bundles On Linear Algebraic Groups
Zev Rosengarten
We study the Picard groups of connected linear algebraic groups, and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every…
Transitivity of Infinite-Dimensional Extensions of Anosov Diffeomorphisms
Zev Rosengarten, Asaf Reich
We consider extensions of Anosov diffeomorphisms of an infranilmanifold by the real vector space R^ω. Our main result, based on the analogous theorem in finite dimensions proven by…