Results 71 to 80 of about 245 (169)

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
doaj   +1 more source

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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On the Normal Stability of Triharmonic Hypersurfaces in Space Forms. [PDF]

J Geom Anal, 2023
Branding V.
europepmc   +1 more source

Geometric algebra generation of molecular surfaces. [PDF]

J R Soc Interface, 2022
Alfarraj A, Wei GW, Wei GW.
europepmc   +1 more source

Clifford Algebra - A Unified Language for Geometric Operations

, 2022
In this paper the Clifford Algebra is introduced and proposed as analternative to Gibbs' vector algebra as a unifying language for geometricoperations on vectors. Firstly, the algebra is constructed using a quotientof the tensor algebra and then its most important properties are proved,including how it enables division between vectors and how it is ...
Gordin, Leo, Hansson, Henrik Taro
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Geometric algebra based recurrent neural network for multi-dimensional time-series prediction. [PDF]

Front Comput Neurosci, 2022
Li Y, Wang Y, Wang Y, Qian C, Wang R.
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