Related papers: A geometric take on Kostant's Convexity Theorem

We show that for a Lie group $G=\R^{n}\ltimes_{\phi} \R^{m}$ with a semisimple action $\phi$ which has a cocompact discrete subgroup $\Gamma$, the solvmanifold $G/\Gamma$ admits a canonical invariant formal (i.e. all products of harmonic…

In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that…

Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_p}$ of the finite field of prime order $p$ and let $F : \mathbf{G} \to \mathbf{G}$ be a Frobenius endomorphism with $G = \mathbf{G}^F$…

Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the…

Let {\Lnk} be the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideals. In 2020 the authors et al. gave a classification of all non 2-step nilpotent Lie algebras of {\Li}. We propose in this paper to…

We consider the action of a real reductive group G on a Kaehler manifold Z which is the restriction of a holomorphic action of the complexified group G^C. We assume that the induced action of a compatible maximal compact subgroup U of G^C…

Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a…

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G X) < dim G for some definable X subset of G then X contains a torsion point of G. Along the way we develop a general theory for…

Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will…

We study a notion of convex cocompactness for discrete subgroups of the projective general linear group acting (not necessarily irreducibly) on real projective space, and give various characterizations. A convex cocompact group in this…

This work builds on the foundation laid by Gordon and Wilson in the study of isometry groups of solvmanifolds, i.e. Riemannian manifolds admitting a transitive solvable group of isometries. We restrict ourselves to a natural class of…

Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…

A commutative associative algebra A with an identity over the field of real numbers which has a basis, where all elements are invertible, is considered in the work. Moreover, among matrixes consisting of the structure constants of A, there…

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial…

Let \phi be a real-valued valuation on the family of compact convex subsets of \mathbb{R}^n and let K be a convex body in \mathbb{R}^n. We introduce the \phi -covariogram g_{K,\phi} of K as the function associating to each x \in…

Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…

We construct a model unifying general relativity and quantum mechanics in a broader structure of noncommutative geometry. The geometry in question is that of a transformation groupoid given by the action of a finite group G on a space E. We…

Many physically important mechanical systems may be described with a Lie group $G$ as configuration space. According to the well-known Noether's theorem, underlying symmetries of the Lie group may be used to considerably reduce the…

This paper extends the Kadison duality between compact convex sets and function systems to the setting of partial convexity. A partially convex set is a set that is convex in a designated set of convex variables when the others are held…