Clifford, J. A. George, C. R. Stoker, G. Briggs, and D. W. Beaty. Lunar and Planetary Institute, 3600 Bay Area Blvd, Houston, TX 77058, [email protected]. NASA Johnson Space Center, Houston, TX 77058, [email protected]. NASA Ames Research Center, Moffet Field, CA 94035, [email protected], gbriggs@ mail.arc.nasa.gov. Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, C...

We present a generalization of the Clifford action for other representations spaces of Spin(n), which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In particular, we have general Bochner identities for them, and an eigenvalue estimate of a Laplace type operator on any associated bundle.

The paper deals with braided Clifford algebras, understood as Chevalley-Kähler deformations of braided exterior algebras. It is shown that Clifford algebras based on involutive braids can be naturally endowed with a braided quantum group structure. Basic group entities are constructed explicitly.

The aim of this paper is to present a new framework for regularization by diffusion. The methods we develop in the sequel can be used to smooth nD images, nD videos, vector fields and orthonormal frame fields in any dimension.1 From a mathematical viewpoint, we deal with vector bundles over Riemannian manifolds and socalled generalized Laplacians. Sections are regularized from heat equations as...

Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that opposite Clifford algebras have to be used also. Based on this mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby ...

The main objective of this paper is to clarify the ontology of DiracHestenes spinor fields (DHSF ) and its relationship with even multivector fields, on a Riemann-Cartan spacetime (RCST) M =(M,g,∇, τg, ↑) admitting a spin structure, and to give a mathematically rigorous derivation of the so called Dirac-Hestenes equation (DHE ) in the case where M is a Lorentzian spacetime (the general case whe...