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...