Related papers: Weingarten integration over noncommutative homogen…
The space of deformations of the integer Heisenberg group under the action of $\textrm{Aut}(H(\mathbb{R}))$ is a homogeneous space for a non-reductive group. We analyze its structure as a measurable dynamical system and obtain mean and…
The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifolds that will play similar roles in the theory of holomorphic…
In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and…
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase…
The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological…
In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…
This article contains a Wiener Lemma for the convolution algebra $\ell^1(\mathbb H,\mathbb C)$ and group $C^\ast$-algebra $C^\ast(\mathbb H)$ of the discrete Heisenberg group $\mathbb H$. At first, a short review of Wiener's Lemma in its…
For a closed cocompact subgroup $\Gamma$ of a locally compact group $G$, given a compact abelian subgroup $K$ of $G$ and a homomorphism $\rho:\hat{K}\to G$ satisfying certain conditions, Landstad and Raeburn constructed equivariant…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
Here we extend the algebro-geometric approach to free probability, started in~\cite{FMcK4,F14}, to general (non)-commutative probability theories. We show that any universal convolution product of moments of independent (non)-commutative…
We discuss the notion of matrix model, $\pi:C(X)\to M_K(C(T))$, for algebraic submanifolds of the free complex sphere, $X\subset S^{N-1}_{\mathbb C,+}$. When $K\in\mathbb N$ is fixed there is a universal such model, which factorizes as…
The leitmotiv of this review is noncommutative principal U(1)-bundles and associated line bundles. In the first part I give a brief introduction to Hopf-Galois theory and its applications, from field extensions to principal group actions. I…
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or…
A general approach to compute the spherical measure of submanifolds in homogeneous groups is provided. We focus our attention on the homogeneous tangent space, that is a suitable weighted algebraic expansion of the submanifold. This space…
We study equivariant embeddings with small boundary of a given homogeneous space $G/H$, where $G$ is a connected, linear algebraic group with trivial Picard group and only trivial characters, and $H \subset G$ is an extension of a connected…
In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not necessarily K\"ahler, we solve the Hermitian-Einstein equation on analytically stable…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
In Gen. Rel. Grav. (36, 111-126 (2004); in press, gr-qc/0410010) we have proposed a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry was developed in terms of a noncommutative algebra…
In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…