相关论文: On Paragrassmann Differential Calculus
The Chevalley-Eilenberg differential calculus and differential operators over N-graded commutative rings are constructed. This is a straightforward generalization of the differential calculus over commutative rings, and it is the most…
A rigid framework for the Cartan calculus of Lie derivatives, inner derivations, functions, and forms is proposed. The construction employs a semi-direct product of two graded Hopf algebras, the respective super-extensions of the deformed…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.
A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular…
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are introduced and investigated. Furthermore,…
A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $ U(1) $ -covariance. Explicit representations of possible $q $-Lie algebras are constructed…
The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus…
Differential calculus on the quantum quaternionic group GL(1,H$_q$) is introduced.
We explore a differential calculus on the algebra of smooth functions on a manifold. The former is `noncommutative' in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus…
We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the…
We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case ($q \rightarrow 1$ limit). The Lie derivative and the contraction operator on forms and…
We show that the bicovariant first order differential calculi on a factorisable semisimple quantum group are in 1-1 correspondence with irreducible representations $V$ of the quantum group enveloping algebra. The corresponding calculus is…
For the two-parameter matrix quantum group GLp,q(2) all bicovariant differential calculi (with a four-dimensional space of 1-forms) are known. They form a one-parameter family. Here, we give an improved presentation of previous results by…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
A review of recent developments in the quantum differential calculus. The quantum group $GL_q(n)$ is treated by considering it as a particular quantum space. Functions on $SL_q(n)$ are defined as a subclass of functions on $GL_q(n)$. The…
An introduction to quantum groups and non-commutative differential calculus (Lecture at the III Workshop on Differential Geometry, Granada, September 1994)
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.