We present some new relations between the Cauchy-Riemann operator on the real Clifford algebra $\mathbb R_n$ of signature $(0,n)$ and slice-regular functions on $\mathbb R_n$. The class of slice-regular functions, which comprises all polynomials with...
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional
For each quadratic form Q in Quad(V) over a given vector space over a field R we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form $x x-Q(x),x...
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Clifford is a 1994 American slapstick black comedy film directed by Paul Flaherty, written by Will Porter (under the alias of "Jay Dee Rock") and Steven
Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) <-> \bigwedg...
Hertfordshire, by Louise's ex-boyfriend Kyle Clifford. The subsequent manhunt lasted until the next day, ending when Clifford was found injured near his home in
Clifford algebra. The square Γ2 of the chirality element is always a scalar, as is immediate by choosing an orthogonal basis ei, and etting Γ = e1 en. In fact, since Γ⊤ = (−1)n
There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection...
Clifford Robert Olson Jr. (January 1, 1940 – September 30, 2011) was a Canadian convicted serial killer who confessed to murdering 11 children, aged between
Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework, which aff...
Definition A Clifford algebra C for a quadratic space V is one that is compatible with V (via σ : V → C) and such that for any other algebra A that is compatible with V (via φ : V → A), there is a unique …
Several Clifford algebras that are covariant under the action of a Lie algebra $g$ can be deformed in a way consistent with the deformation of $Ug$ into a quantum group (or into a triangular Hopf algebra) $U_qg$, i.e. so as to remain covariant unde...
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Clifford algebras provide an excellent generalization of rotations, spin, and even more general conformal mappings/transformations (think of the M ̈obius transformations from the problem sets).
This preserves the defining ideal so descends to a linear automorphism of the Clifford algebra. This automorphism is not compatible with the algebra structure in the usual sense.
Points: 189 | Comments: 71 | Author: beefman
Margaret Mary Clifford (Irish: Mairéad Ní Clúmháin, later Comer; 1896–20 April 1982), from Tralee, County Kerry, was an Irish republican and officer in
Abstract wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geomet-ric …
This paper is intended to investigate Grassmann and Clifford algebras over Peano spaces, introducing their respective associated extended algebras, and to explore these concepts also from the counterspace viewpoint. The exterior (regressive) algebr...
Geometric Algebra for Python (⭐ 851)
Since the Kings are currently tanking what do y'all think Nique Clifford's role would be long term? He's currently getting massive minutes and a good amount of shots each game and is looking like a po...
SQL queries used for my webinar, Spatial SQL Isn't Scary (⭐ 9)
Multivector quantum mechanics utilizes wavefunctions which are Clifford aggregates (e.g. sum of scalar, vector, bivector). This is equivalent to multi- spinors constructed of Dirac matrices, with the representation independent form of the generator...
Discover the historic charm of White Cliffs Function Facilities in Northborough, MA. Spacious function room, elegant woodwork, tin ceilings, centrally located dance floor. Contact us for unforgettable …
We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n graded commutative associative algebra. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford...
Hi guys, I have started a channel to explore different applications of Clifford/Geometric Algebra to math and physics, and I want to share it with you. This particular video is about solving systems ...
In this work, we investigate the average information scrambling and nonlocal magic generation properties of random Clifford encoding-decoding circuits perturbed by local noise. We quantify these with the bipartite algebraic out-of-time order correlat...
This paper investigates centralizers and twisted centralizers in degenerate and non-degenerate Clifford (geometric) algebras. We provide an explicit form of the centralizers and twisted centralizers of the subspaces of fixed grades, subspaces determi...
PhysioNet Cardiovascular Signal Toolbox (⭐ 129)
Let $κ$ be a commutative ring containing $2^{-1}$. In this paper, we prove the Comes-Kujawa's conjecture on a $κ$-basis of cyclotomic oriented Brauer-Clifford supercategory. As a by-product, we prove that the cyclotomic walled Brauer-Clifford super...
T. Kobayashi conjectured in the 36th Geometry Symposium in Japan (1989) that a homogeneous space G/H of reductive type does not admit a compact Clifford-Klein form if rank G - rank K < rank H - rank K_H. We solve this conjecture affirmatively. We app...
The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators...
The Clifford hierarchy is a fundamental structure in quantum computation whose mathematical properties are not fully understood. In this work, we characterize permutation gates -- unitaries which permute the $2^n$ basis states -- in the third level o...
Maxwell Frank Clifford (6 April 1943 – 10 December 2017) was an English publicist and convicted sex offender who was particularly associated with promoting
largest cliff dwelling in North America. The structure built by the Ancestral Puebloans is located in Mesa Verde National Park in their former homeland
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Super Bitch (Italian: Si può essere più bastardi dell'ispettore Cliff?, lit. 'Can anyone be more of a bastard than Inspector Cliff?') is a 1973 Italian-British
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In this work we...
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