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Connection Speed
Connection may refer to: Mathematics *Connection (algebraic framework) *Connection (mathematics), a way of specifying a derivative of a geometrical object along a vector field on a manifold *Connection (affine bundle) * Connection (composite bundle) *Connection (fibred manifold) *Connection (principal bundle), gives the derivative of a section of a principal bundle *Connection (vector bundle), differentiates a section of a vector bundle along a vector field *Cartan connection, achieved by identifying tangent spaces with the tangent space of a certain model Klein geometry *Ehresmann connection, gives a manner for differentiating sections of a general fibre bundle *Electrical connection, allows the flow of electrons *Galois connection, a type of correspondence between two partially ordered sets *Affine connection, a geometric object on a smooth manifold which connects nearby tangent spaces *Levi-Civita connection, used in differential geometry and general relativity; differentiates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connection (algebraic Framework)
Geometry of quantum systems (e.g., noncommutative geometry and supergeometry) is mainly phrased in algebraic terms of modules and algebras. Connections on modules are generalization of a linear connection on a smooth vector bundle E\to X written as a Koszul connection on the C^\infty(X)-module of sections of E\to X. Commutative algebra Let A be a commutative ring and M an ''A''-module. There are different equivalent definitions of a connection on M. First definition If k \to A is a ring homomorphism, a k-linear connection is a k-linear morphism : \nabla: M \to \Omega^1_ \otimes_A M which satisfies the identity : \nabla(am) = da \otimes m + a \nabla m A connection extends, for all p \geq 0 to a unique map : \nabla: \Omega^p_ \otimes_A M \to \Omega^_ \otimes_A M satisfying \nabla(\omega \otimes f) = d\omega \otimes f + (-1)^p \omega \wedge \nabla f. A connection is said to be integrable if \nabla \circ \nabla = 0, or equivalently, if the curvature \nabla^2: M \to \Omeg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |