Related papers: Noncommutative Differential Calculus: Quantum Grou…
We develop the foundations of Algebraic Stochastic Calculus, with an aim to replacing what is typically referred to as Stochastic Calculus by a purely categorical version thereof. We first give a sheaf theoretic reinterpretation of…
We consider GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…
We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups…
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…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…
We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
We investigate the $q$-deformation of the BRST algebra, the algebra of the ghost, matter and gauge fields on one spacetime point using the result of the bicovariant differential calculus. There are two nilpotent operations in the algebra,…
Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.
Stochastic processes on totally disconnected topological groups are investigated. In particular they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance…
In this follow-up of the article: Quantum Group of Isometries in Classical and Noncommutative Geometry(arXiv:0704.0041) by Goswami, where quantum isometry group of a noncommutative manifold has been defined, we explicitly compute such…
Two differential calculi are developped on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a…
We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…
The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…
We develop a pseudo-differential Weyl calculus on nilpotent Lie groups which allows one to deal with magnetic perturbations of right invariant vector fields. For this purpose we investigate an infinite-dimensional Lie group constructed as…
This is the first in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we study theories of supercommutative algebras…
We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We…