Results 71 to 80 of about 251 (170)

Structural Properties of The Clifford–Weyl Algebra ${𝒜}_q^{\pm }$

Mathematics
The Clifford–Weyl algebra 𝒜q±, as a class of solvable polynomial algebras, combines the anti-commutation relations of Clifford algebras 𝒜q+ with the differential operator structure of Weyl algebras 𝒜q−. It exhibits rich algebraic and geometric properties.
Jia Zhang, Gulshadam Yunus
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Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries [PDF]

, 2006
Given a quadratic form on a vector space, the geometric algebra of the corresponding pseudo-euclidean space is defined in terms of a simple set of rules which characterizes the geometric product of vectors. We develop geometric algebra in such a way that it augments, but remains fully compatible with, the more traditional tools of matrix algebra ...
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Clifford (Geometric) Algebra Wavelet Transform

, 2013
While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be constructed using the similitude group $SIM(n)$.
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Geometric (Clifford) algebra and its applications

, 2006
M.Sc. Thesis (January 2006), 68 pages.
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Hecke algebras as subalgebras of Clifford geometric algebras of multivectors

, 1997
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra H_{K}(n+1,q) if the bilinear form B is chosen appropriately. This shows, that q-quantization can be generated by Clifford
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Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm's hidden variables. [PDF]

Sci Rep, 2022
Santilli RM, Sobczyk G.
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Clifford Algebra, Isoparametric Foliation and Related Geometric Constructions

Based on representation theory of Clifford algebra, Ferus, Karcher and Münzner constructed a series of isoparametric foliations. In this paper, we will survey recent studies on isoparametric hypersurfaces of OT-FKM type and investigate related geometric constructions with mean curvature flow.
Qian, Chao, Tang, Zizhou
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Differentials of the basis in Clifford Geometric Algebra

Journal of AppliedMath
In this paper we discuss the dynamic effects of the varying frames. The differential of frame or basis vectors is always equivalent to a linear transformation of the frame, and the linear transformation is not the same in different contexts. In differential geometry, the linear transformation is the connection operator.
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On the Normal Stability of Triharmonic Hypersurfaces in Space Forms. [PDF]

J Geom Anal, 2023
Branding V.
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Geometric algebra generation of molecular surfaces. [PDF]

J R Soc Interface, 2022
Alfarraj A, Wei GW, Wei GW.
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