16 citations · 29 across the 14 of their papers we have counts for
6 papers · 1 filter
On the orbit space of a three-dimensional compact linear Lie group
O. G. Styrt
We study the question of whether the topological quotient of a real linear representation of a simple three-dimensional compact Lie group is a manifold. We obtain an upper bound fo…
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.
On the orbit space of an irreducible representation of the special unitary group
O. G. Styrt
We prove that the quotient of an irreducible representation of a special unitary group of rank greater than 1 cannot be a smooth manifold.
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…