208 research outputs found
Tits type alternative for groups acting on toric affine varieties
Given a toric affine algebraic variety and a collection of one-parameter
unipotent subgroups of which are
normalized by the torus acting on , we show that the group generated by
verifies the following alternative of Tits' type: either
is a unipotent algebraic group, or it contains a non-abelian free subgroup. We
deduce that if is -transitive on a -orbit in , then contains a
non-abelian free subgroup, and so, is of exponential growth.Comment: 24 pages. The main result strengthened, the proof of Proposition 4.8
written in more detail; some references added; the referee remarks taken into
account; the title change
Classification of reductive real spherical pairs II. The semisimple case
If is a real reductive Lie algebra and is a subalgebra, then is called
real spherical provided that
for some choice of a minimal parabolic subalgebra . In this paper we classify all real spherical pairs where is semi-simple but not simple and
is a reductive real algebraic subalgebra. The paper is based on
the classification of the case where is simple (see
arXiv:1609.00963) and generalizes the results of Brion and Mikityuk in the
(complex) spherical case.Comment: Extended revised version. Section 6 and Appendix B are new. To appear
in Transformation Groups. 40
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Mini-Workshop: Algebraic and Analytic Techniques for Polynomial Vector Fields
Polynomial vector fields are in the focus of research in various areas of mathematics and its applications. As a consequence, researchers from rather different disciplines work with polynomial vector fields. The
main goal of this mini workshop was to create new and consolidate existing interdisciplinary exchange on the subject
Branch Rings, Thinned Rings, Tree Enveloping Rings
We develop the theory of ``branch algebras'', which are infinite-dimensional
associative algebras that are isomorphic, up to taking subrings of finite
codimension, to a matrix ring over themselves. The main examples come from
groups acting on trees.
In particular, for every field k we construct a k-algebra K which (1) is
finitely generated and infinite-dimensional, but has only finite-dimensional
quotients;
(2) has a subalgebra of finite codimension, isomorphic to ;
(3) is prime;
(4) has quadratic growth, and therefore Gelfand-Kirillov dimension 2;
(5) is recursively presented;
(6) satisfies no identity;
(7) contains a transcendental, invertible element;
(8) is semiprimitive if k has characteristic ;
(9) is graded if k has characteristic 2;
(10) is primitive if k is a non-algebraic extension of GF(2);
(11) is graded nil and Jacobson radical if k is an algebraic extension of
GF(2).Comment: 35 pages; small changes wrt previous versio
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
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