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The topology of the embedding of the coadjoint orbits of the unitary group U(H) of an in-finite dimensional complex Hilbert space H, as canonically determined subsets of the B-space T_s of symmetric trace class operators, is investigated.…

Let $H$ be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold $X$ and a real algebraic bundle $\mathcal{E}$ on $X$. Let $\mathfrak{h}$ be the Lie algebra of $H$. Let…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

Recently, S. Meljanac proposed a construction of a class of examples of an algebraic structure with properties very close to the Hopf algebroids $H$ over a noncommutative base $A$ of other authors. His examples come along with a subalgebra…

This article is a continuation of [Kub18], which proves that if a $3$-dimensional affine normal quasihomogeneous $SL(2)$-variety $E$ is toric, then it has an equivariant resolution of singularities given by an invariant Hilbert scheme…

Let V be a finite dimensional representation of the connected complex reductive group H. Denote by G the derived subgroup of H and assume that the categorical quotient of V by G is one dimensional. In this situation there exists a…

A visible action on a complex manifold is a holomorphic action that admits a $J$-transversal totally real submanifold $S$. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism $\sigma $ such…

We prove two rigidity theorems on holomorphic isometries into homogeneous bounded domains. The first shows that a K\"ahler-Ricci soliton induced by the homogeneous metric of a homogeneous bounded domain is trivial, i.e. K\"ahler-Einstein.…

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is…

A $k$-reflection of the $n$-dimensional complex hyperbolic space ${\rm H}_{\C}^n$ is an element in ${\rm U}(n,1)$ with negative type eigenvalue $\lambda$, $|\lambda|=1$, of multiplicity $k+1$ and positive type eigenvalue $1$ of multiplicity…

We prove a number of results concerning monomorphisms, epimorphisms, dominions and codominions in categories of coalgebras. Examples include: (a) representation-theoretic characterizations of monomorphisms in all of these categories that…

In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing…

Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. We construct all…

We study the problem of determining, for a polynomial function $f$ on a vector space $V$, the linear transformations $g$ of $V$ such that $f g = f$. In case $f$ is invariant under a simple algebraic group $G$ acting irreducibly on $V$, we…

We study three different topologies on the moduli space $\mathscr{H}^{\rm loc}_m$ of equivariant isometry classes of $m$-dimensional locally homogeneous Riemannian spaces. As an application, we provide the first examples of locally…

A commutative residuated lattice A is said to be subidempotent if the lower bounds of its neutral element e are idempotent (in which case they naturally constitute a Brouwerian algebra A*). It is proved here that epimorphisms are surjective…

Let $X$ be a smooth compact connected manifold. Let $G=\mbox{Diff}\, X$ be the group of diffeomorphisms of $X$, equipped with the $C^\infty$-topology, and let $H$ be the stabilizer of some point in $X$. Then the inclusion $H\to G$, which is…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

Considering uniform hypergraphs, we prove that for every non-negative integer $h$ there exist two non-negative integers $k$ and $t$ with $k\leq t$ such that two $h$-uniform hypergraphs ${\mathcal H}$ and ${\mathcal H}'$ on the same set $V$…

We study algebraic and topological properties of subsemigroups of the hyperspace exp(G) of non-empty compact subsets of a topological group G endowed with the Vietoris topology and the natural semigroup operation. On this base we prove that…