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...
No description (⭐ 174)
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...
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...
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...