16 citations · 29 across the 14 of their papers we have counts for
14 papers
Embeddability of joinpowers, and minimal rank of partial matrices
A. Skopenkov, O. Styrt
A general position map of a -dimensional simplicial complex to a -dimensional manifold (for , of a graph to a surface) is a -embedding if $|fσ\c…
Convergence in distribution of the product of random variables from an independent sample on a compact algebraic group
O. G. Styrt
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample si…
Elements of a Lie algebra acting nilpotently in all its representations
O. G. Styrt
An equivalent condition for an element of a Lie algebra acting nilpotently in all its representations is obtained. Namely, it should belong to the derived algebra and go via factor…
Orthogonality graphs of matrices over commutative rings
O. G. Styrt
The paper is devoted to studying the orthogonality graph of the matrix ring over a commutative ring. It is proved that the orthogonality graph of the ring of matrices with size gre…
On matrix sets invariant under conjugation and taking linear combinations of commuting elements
O. G. Styrt
Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously incl…
Topological and homological properties of the orbit space of a simple three-dimensional compact linear Lie group
O. G. Styrt
The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple th…
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 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…