Related papers: Describing Curved Spaces by Matrices

An analysis of the boundary representations and C$^*$-envelopes of some finite-dimensional operator systems $\mathcal R$ is undertaken by considering relationships between operator-theoretic properties of a $d$-tuple $\mathfrak…

In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…

We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…

This paper builds on our previous work in which we showed that, for all connected semisimple linear Lie groups $G$ acting on a non-compactly causal symmetric space $M = G/H$, every irreducible unitary representation of $G$ can be realized…

By a theorem of Mclean, the deformation space of an associative submanifold Y of an integrable G_2 manifold (M,\phi) can be identified with the kernel of a Dirac operator D:\Omega^{0}(\nu) -->\Omega^{0}(\nu) on the normal bundle \nu of Y.…

We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…

The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the…

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

A geometrical interpretation of Schr\"odinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum…

This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…

We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces,…

In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and consider the class of matrices that can be approached in the operator norm by matrices with a…

We develop a formalism that allows us to write actions for multiple D-branes with manifest general covariance. While the matrix coordinates of the D-branes have a complicated transformation law under coordinate transformations, we find that…

The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local…

Unfolded equations of motion for N = 1, D = 4 scalar supermultiplet are presented. We show how the superspace formulation emerges from the unfolded formulation. To analyze supersymmetric unfolded equations we extend the \sigma_-cohomology…

It is shown that each linear operator on a separable Hilbert space which generates a finite type I von Neumann algebra has, up to unitary equivalence, a unique representation as a direct integral of inflations of mutually unitary…

For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian…

Covariance of a quantum space with respect to a quantum enveloping algebra ties the deformation of the multiplication of the space algebra to the deformation of the coproduct of the enveloping algebra. Since the deformation of the coproduct…

We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…