Related papers: Field and forms on $\rho$-algebras
In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. A special inequality which…
We give an explicit description of the set of all factorization structures, or twisting maps, existing between the algebras k^2 and k^2, and classify the resulting algebras up to isomorphism. In the process we relate several different…
Recently V. Ginzburg proved that Calogero phase space is a coadjoint orbit for some infinite dimensional Lie algebra coming from noncommutative symplectic geometry. In this note we generalize this argument to specific quotient varieties of…
We give a general construction of extended moduli spaces of topological D-branes as non-commutative algebraic varieties. This shows that noncommutative symplectic geometry in the sense of Kontsevich arises naturally in String Theory.
Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type…
This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with…
Identities pertaining to the de Rham codifferential $\delta$ in differential geometry are scattered in the literature. This article gathers such formulas involving usual differential operators (Lie derivative, Schouten-Nijenhuis bracket,…
Motivated by the search for new examples of ``noncommutative manifolds'', we study the noncommutative geometry (in the sense of Connes) of the group C*-algebra of the three dimensional discrete Heisenberg group. We present a unified…
The goal of this paper is to define a notion of non-commutative Gelfand duality. Using techniques from derived algebraic geometry, we show that the category of rings is anti-equivalent to a subcategory of pre-ringed sites, inspired by…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
A natural extension of the standard model within non-commutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
In this paper, we start the investigation of a new natural approach to "unifying" noncommutative gauge field theories (NCGFT) based on approximately finite-dimensional ($AF$) $C^*$-algebras. The defining inductive sequence of an $AF$…
We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf…
In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of…
We study Lie-Rinehart algebra structures in the framework provided by a duality pairing of modules over a unital commutative associative algebra. Thus, we construct examples of Lie brackets corresponding to a fixed anchor map whose image is…
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known…
A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…
We first introduce the Wigner-Weyl-Moyal formalism for a theory whose phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie algebras and to supersymmetric theories. It turns out that the non-commutativity leads to a…
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie…
We describe how noncommutative function algebras built from noncommutative functions in the sense of \cite{K-VV2014} may be studied as subalgebras of homogeneous $C^{*}$-algebras.