Topic
Bivector
About: Bivector is a research topic. Over the lifetime, 319 publications have been published within this topic receiving 5120 citations. The topic is also known as: 2-vector.
Papers published on a yearly basis
Papers
TL;DR: The notion of real structure in spectral geometry was introduced in this paper, motivated by Atiyah's KR•theory and by Tomita's involution J. It allows us to remove two unpleasant features of the Connes-Lott description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.
Abstract: We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR‐theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the ‘‘Connes–Lott’’ description of the standard model, namely, the use of bivector potentials and the asymmetry in the Poincare duality and in the unimodularity condition.
711 citations
TL;DR: A quasi-Poisson manifold is a -manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in associated to an inner product as mentioned in this paper.
Abstract: A quasi-Poisson manifold is a -manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.
234 citations
1 Nov 1965
TL;DR: Vector analysis approach to algebra of rotations with applications to least-squares rotation and rigid body motion is presented in this article, where the vector analysis approach is applied to least square rotation.
Abstract: Vector analysis approach to algebra of rotations with applications to least-squares rotation and rigid body motion
151 citations
Posted Content•
TL;DR: A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in the inner product.
Abstract: A quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in $\wedge^3 \g$ associated to an invariant inner product. We introduce the concept of the fusion for such manifolds, and we relate quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.
108 citations
TL;DR: In this article, the Evens-Lu Poisson structures on the variety of Lagrangian Grassmannians and on the de Concini-Procesi compactifications are interpreted in terms of the behavior of splittings under Courant morphisms.
Abstract: Given a manifold M with an action of a quadratic Lie algebra , such that all stabilizer algebras are coisotropic in , we show that the product becomes a Courant algebroid over M. If the bilinear form on is split, the choice of transverse Lagrangian subspaces of defines a bivector field π on M, which is Poisson if is a Manin triple. In this way, we recover the Poisson structures of Lu-Yakimov, and in particular the Evens-Lu Poisson structures on the variety of Lagrangian Grassmannians and on the de Concini-Procesi compactifications. Various Poisson maps between such examples are interpreted in terms of the behavior of Lagrangian splittings under Courant morphisms.
70 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 10 |
| 2020 | 9 |
| 2019 | 9 |
| 2018 | 10 |
| 2017 | 17 |
| 2016 | 8 |