Computing Optimal Descriptions of Stratifications of Actions of Compact Lie Groups
نویسنده
چکیده
We provide a constructive approach to the stratification of the representationand the orbit space of linear actions of compact Lie groups contained in GLn(R) on R n and we show that any d-dimensional stratum, respectively, its closure can be described by d sharp, respectively, relaxed polynomial inequalities and that d is also a lower bound for both cases. Strata of the representation space are described as differences of closed sets given by polynomial equations while d-dimensional strata of the orbit space are represented by means of polynomial equations and inequalities. All algorithms have been implemented in SINGULAR V2.0.
منابع مشابه
Orbit Spaces Arising from Isometric Actions on Hyperbolic Spaces
Let be a differentiable action of a Lie group on a differentiable manifold and consider the orbit space with the quotient topology. Dimension of is called the cohomogeneity of the action of on . If is a differentiable manifold of cohomogeneity one under the action of a compact and connected Lie group, then the orbit space is homeomorphic to one of the spaces , , or . In this paper we suppo...
متن کاملLattice of full soft Lie algebra
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a ...
متن کاملStratifications Associated to Reductive Group Actions on Affine Spaces
For a complex reductive group G acting linearly on a complex affine space V with respect to a characterρ, we show two stratifications ofV associated to this action (and a choice of invariant inner product on the Lie algebra of the maximal compact subgroup ofG) coincide. The first is Hesselink’s stratification by adapted 1-parameter subgroups and the second is the Morse theoretic stratification ...
متن کاملIndex Theory for Actions of Compact Lie Groups on C-algebras
We study the index theory for actions of compact Lie groups on C∗-algebras with an emphasis on principal actions. Given an invariant semifinite faithful trace on the C-algebra we obtain semifinite spectral triples. For circle actions we consider the relation to the dual Pimsner-Voiculescu sequence. On the way we show that the notions “saturated” and “principal” are equivalent for actions by com...
متن کاملOn Minimal, Strongly Proximal Actions of Locally Compact Groups
Minimal, strongly proximal actions of locally compact groups on compact spaces, also known as boundary actions, were introduced by Furstenberg in the study of Lie groups. In particular, the action of a semi-simple real Lie group G on homogeneous spaces G/Q where Q ⊂ G is a parabolic subgroup, are boundary actions. Countable discrete groups admit a wide variety of boundary actions. In this note ...
متن کامل