16 citations · 26 across the 6 of their papers we have counts for
6 papers
Topological and homological properties of the orbit space of a compact linear Lie group with commutative connected component
O. G. Styrt
The problem in question is whether the quotient space of a compact linear group is a topological manifold and whether it is a homological manifold. In the paper, the case of an inf…
The existence of a semialgebraic continuous factorization map for some compact linear groups
O. G. Styrt
It is proved that each of compact linear groups of one special type admits a semialgebraic continuous factorization map onto a real vector space.
On the orbit spaces of irreducible representations of simple compact Lie groups of types B, C, and D
O. G. Styrt
It is proved that the orbit space of an irreducible representation of a simple connected compact Lie group of type B, C, or D can be a smooth manifold only in two cases.
The simplest stationary subalgebras, for compact linear Lie algebras
O. G. Styrt
Sufficient conditions are obtained for the existence of a vector with a one-dimensional or simple three-dimensional stationary subalgebra for an irreducible compact linear Lie alge…
On the orbit space of a compact linear Lie group with commutative connected component
O. G. Styrt
This paper is devoted to the study of topological quotients of compact linear Lie groups. More precisely, it investigates the question of when such a quotient is a topological or a…
The existence of a polynomial factorization map for some compact linear groups
O. G. Styrt
It is proved that each of compact linear groups of one special type admits a polynomial factorization map onto a real vector space. More exactly, the group is supposed to be non-co…