Topic
Two-form
About: Two-form is a research topic. Over the lifetime, 354 publications have been published within this topic receiving 9193 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, a general theory of non-commutative differential geometry on quantum groups is developed, where bicovariant bimodules as objects analogous to tensor bundles over Lie groups are studied.
Abstract: The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles over Lie groups are studied. Tensor algebra and external algebra constructions are described. It is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra, so the external derivative of higher order differential forms is well defined and obeys the usual properties. The proper form of the Cartan Maurer formula is found. The vector space dual to the space of left-invariant differential forms is endowed with a bilinear operation playing the role of the Lie bracket (commutator). Generalized antisymmetry relation and Jacobi identity are proved.
1,343 citations
Book•
19 Dec 1990
TL;DR: The Cartan-Khler theory of linear differential systems has been applied to the study of exterior differential systems as mentioned in this paper, where the characteristic variety prolongation theory applications of commutative algebra and algebraic geometry are studied.
Abstract: Basic theorems Cartan-Khler theory linear differential systems the characteristic variety prolongation theory applications of commutative algebra and algebraic geometry to the study of exterior differential systems partial differential equations linear differential operators.
936 citations
1 Jan 1991
TL;DR: In this paper, a differntial calculus on the quantum hyperplane covariant with respect to the action of the quantum group GLq(n) is developed, which is a concrete example of noncommutative differential geometry.
Abstract: We develop a differntial calculus on the quantum hyperplane covariant with respect to the action of the quantum group GLq(n). This is a concrete example of noncommutative differential geometry. We describe the general constraints for a noncommutative differential calculus and verify that the example given here satisfies all these constraints. We also discuss briefly the integration over the quantum plane.
726 citations
561 citations
31 May 1985
TL;DR: In this paper, a self-contained introductory textbook on the calculus of differential forms and modern differential geometry is presented, focusing on applications and geometrical reasoning to give results and concepts a precise but intuitive meaning without getting bogged down in analysis.
Abstract: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.
378 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 2 |
| 2019 | 4 |
| 2017 | 4 |
| 2016 | 7 |
| 2015 | 12 |
| 2014 | 8 |