geometry, a Clifford module bundle, a bundle of Clifford modules or just Clifford module is a vector bundle whose fibers are Clifford modules, the representations...

In mathematics, a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the...

In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field...

) . {\displaystyle {\mathrm {Spin} }(n).} Clifford bundle Clifford module bundle Orthonormal frame bundle Spin geometry Spinor Spinor representation...

projective module over C∞(X), and by Swan's theorem, every projective module is isomorphic to the module of sections of some vector bundle; the category...

space Cayley–Dickson construction Classification of Clifford algebras Clifford analysis Clifford module Complex spin structure Dirac operator Exterior algebra...

combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with...

(up to isomorphism) irreducible representation (also called simple Clifford module), commonly denoted by Δ, of dimension 2[n/2]. Since the Lie algebra...

" — Epitaph Bessel–Clifford function Clifford's principle Clifford analysis Clifford gates Clifford bundle Clifford module Clifford number Motor Rotor...

of the theorem. Let π : E → M {\displaystyle \pi :E\to M} be a clifford module bundle. Assume a compact Lie group G acts on both E and M so that π {\displaystyle...

5𝝅 isoclines. The bundle of 12 Clifford parallel decagon fibers is divided into a bundle of 12 left pentagon fibers and a bundle of 12 right pentagon...

gauge theory. Only in the late 1980s, when QFT was reformulated in fiber bundle language for application to problems in the topology of low-dimensional...

module over a semisimple ring is semisimple. (Proof: A free module over a semisimple ring is semisimple and any module is a quotient of a free module...

mentioned above. For modules over a general (commutative) ring, not every module is free. For example, Z/nZ is not a free abelian group (Z-module). The tensor...

in an entirely conventional way. It acts naturally on the Clifford bundle; the Clifford bundle is the space in which the spinors live. The general exploration...

isomorphic[clarification needed] to the fiber at p of the dual bundle of the kth exterior power of the tangent bundle of M. That is, β {\displaystyle \beta } is also...

sugars for new foliage growth. Food portal Wikibooks Cookbook has a recipe/module on Rhubarb Rhubarb Cake at the Wikibooks Cookbook subproject Rhubarb Crumble...

circles), a fact that is important in the study of S3 as a fiber bundle over S2 (the Hopf bundle). The surface described above, given the relative topology...

analogy between projective modules and vector bundles. The Quillen–Suslin theorem asserts that any finitely generated projective module over k[T1, ..., Tn] (k...

affine representations (i.e., affine modules) of the gauge transformations can be classified as sections of a jet bundle satisfying certain properties. There...

Tensor product of R-algebras Clifford module A representation of a Clifford algebra which gives a realisation of a Clifford algebra as a matrix algebra...

Springer 2008 with D. Eisenbud: Betti numbers of graded modules and cohomology of vector bundles, Journal of the American Mathematical Society, vol. 22...

algebras of T(V). These include the exterior algebra, the symmetric algebra, Clifford algebras, the Weyl algebra and universal enveloping algebras. The tensor...

Seminar his "Algèbres de Clifford et periodicité des groupes πK(BO))". The topic was taken up again in 1964 as Clifford modules by Bott and Atiyah with...

R {\displaystyle R} -module. Geometrically, this means an invertible fractional ideal can be interpreted as rank 1 vector bundle over the affine scheme...

For the non-free case, this generalizes to the notion of the length of a module. The uniquely defined dimension of every connected topological manifold...

SU(3) cannot be the trivial bundle SU(2) × S5 ≅ S3 × S5, and therefore must be the unique nontrivial (twisted) bundle. This can be shown by looking...

and later the same year Lucas Birdeau, Kevin Hakman, Michael Peachey and Clifford Yeh described a single-page application implementation in US patent 8,136...

algebra of finite-dimensional vector bundles and those of the exterior algebra of finitely generated projective modules, by the Serre–Swan theorem. More general...

displaying short descriptions of redirect targets Orientation of a vector bundle – Generalization of an orientation of a vector space Pseudovector – Physical...