Lie group
Equivariant geometric K-homology for compact Lie group actions
... In the case of a compact Lie group, equivariant vector bundles are easy to come by, and therefore the work is much easier than in the case of a discrete proper action. We will in part follow closely the ...
25
Reduced Gutzwiller formula with symmetry: case of a Lie group
... The purpose of this work is to give semi-classical spectral asymptotics of a quantum Hamil- tonian on R 2d reduced by a compact Lie group of symmetry G. We will interpret coefficients in terms of reduced ...
25
Associating Uncertainty to Extended Poses for on Lie Group IMU Preintegration with Rotating Earth
... Preintegrating IMU is an alternative to the standard inertial measurement integration which has de facto been adopted in optimization-based estimation framework such as GTSAM [24] and OKVIS [25]. It was initiated by [26] ...
17
Absolute humanoid localization and mapping based on IMU Lie group and fiducial markers
... proposed Lie group comprising the full IMU delta ...the Lie theory layer, our approach to Jacobians and uncertainty propagation is more compact and ...our Lie formulation easily generalizes to ...
8
Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds
... a Lie group structure on O(M, K) is compatible with evalua- tions if it satisfies the assumptions of the preceding ...complex Lie group structure on the group O(M, K) which is ...
40
Sensitivity analysis for flexible multibody systems formulated on a Lie group
... The Lie group framework offers a number of advantages for the analysis of systems with large rota- tions variables [4, 5], e.g. for finite element models of systems with rigid bodies, kinematic joints, ...
2
Differential invariants of a Lie group action: syzygies on a generating set
... In Section 1 we extract from the books of Olver (1986, 1995) the essential ma- terial we need for describing actions and their prolongations. In Section 2 we define invariantization and normalized invariants for the ...
53
Differential graded Lie groups and their differential graded Lie algebras
... differential Lie algebra A DGLA is a GLA endowed with a square 0 degree 1 ...a group object in the category of differential graded ...that Lie commutes with ...a group object in the category ...
47
Towards coordination algorithms on compact Lie groups
... The two approaches considered in the present work to generalize the results of Section 3 to mechanical models - consensus tracking and energy shaping - are well-known in the control liter- ature. The viewpoint adopted in ...
58
Spin representations for Hermitian Lie groups
... The uniformization theorem yields a bijection between M g,s and isomorphism classes of hyperbolic structures on S with cusps at each puncture. The holonomy of such a hyper- bolic structure is a maximal homomorphism π 1 ...
116
Monomial bases and pre-Lie structure for free Lie algebras
... The Lie algebra of a real connected Lie group G admits a compatible pre-Lie structure if and only if G admits a left-invariant affine structure [5, Proposition ...
30
On Lie algebra crossed modules
... to group level. The relation of continuous group cohomology, cohomology as a topological space and Lie algebra cohomology of the Lie algebra of a Lie group is given by the ...
25
Invariant Smoothing on Lie Groups
... These approaches are focused on leveraging the intrinsic tools of a given structure of the state space (Riemannian manifold or Lie group). For instance in [14], the proposed algorithm only required the ...
9
Coordinated motion design on Lie groups
... the Lie group; the ac- tual values of the relative positions on the Lie group, as long as they are compatible with the coordinated motion, are not con- ...the Lie group which are ...
12
Coordination on Lie groups
... the group SE(2) are ...in Lie group notation in ...Euclidean group in the plane G = SE(2) describes all planar rigid body motions (translations and ...
5
Hall basis of twisted Lie algebras
... Remark. If we suppose that all elements of X are of degree 1, we recover Barratt’s definition of a free twisted (associative) algebra and Lie algebra. 4. Lyndon words Preliminary remark. One can ask - and we are ...
21
Représentations de groupes de Lie et fonctionnement géométrique du cerveau
... The success of Euclidean-symmetry-based arguments for describing flat parts of V1 makes it quite natural, from a neural point of view, to wonder whether in curved regions of V1, the layout of orientation preferences ...
274
Cyclic elements in semisimple lie algebras
... In Section 3 we introduce the notion of a reducing subalgebra for a nilpotent element e of even depth in a simple Lie algebra g. It is a semisimple subalgebra q, normalized by s, such that Z(s)(q ∩ g −d ) is ...
34
Indices analytiques à support compact pour des groupoïdes de Lie
... Le but de la th´eorie de l’indice est grosso modo d’obtenir des inva- riants g´eom´etriques des ”espaces” `a partir des donn´ees analytiques. Clas- siquement on utilise les op´erateurs appel´es pseudodiff´erentiels et ...
139
Algèbres de Hopf d'arbres et structures pré-Lie
... produit tensoriel H ⊗ H CK , qui en fait une algèbre de Hopf dont le dual gradué est isomorphe à l’algèbre enveloppante du produit semi-direct des deux algèbres de Lie considérées. Nous montrons que l’espace ...
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