When Einstein was thinking about the theory of general relativity based on the elimination of especial relativity constraints (especially the geometric relationship of space and time), he understood the first limitation of especial relativity is ignoring changes over time. Because in especial relativity, only the curvature of the space was considered. Therefore, tensor calculations should be to...

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The purpose of this article is to develop the notions of amenabilityfor vector valued group algebras. We prove that L1(G, A) is approximatelyweakly amenable where A is a unital separable Banach algebra. We givenecessary and sufficient conditions for the existence of a left invariant meanon L∞(G, A∗), LUC(G, A∗), WAP(G, A∗) and C0(G, A∗).

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. introduce twisted cartesian product two algebras according to linear representations by infinitesimal transformations. also exhibit double extension process algebra which allows us get all simply connected groups with bi-invariant symplectic connections. All constructed performin...

There is a well known one–parameter family of left invariant CR structures on SU(2) ∼= S. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

We show that the groups of finite energy loops and paths (that is, those Sobolev class H 1 ) with values in a compact connected Lie group, as well their central extensions, satisfy an amenability-like property: they admit left-invariant mean on space bounded functions uniformly continuous regard to metric. Every strongly unitary representation π such group (which we call skew-amenable) has conj...