Results 11 to 20 of about 19,016 (193)
Computational and Applied Mathematics, 2021 In this paper, we solve the problem of computing the inverse in Clifford algebras of arbitrary dimension. We present basis-free formulas of different types (explicit and recursive) for the determinant, other characteristic polynomial coefficients ...
Shirokov, D. S.
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Idempotents of Clifford Algebras
European Physical Journal D, 2003 A classification of idempotents in Clifford algebras C(p,q) is presented. It is shown that using isomorphisms between Clifford algebras C(p,q) and appropriate matrix rings, it is possible to classify idempotents in any Clifford algebra into continuous ...
Ablamowicz, R. +3 more
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Shorter quantum circuits via single-qubit gate approximation [PDF]
Quantum, 2023 We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a factor of 7/9 ...
Vadym Kliuchnikov +4 more
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Contractions on ranks and quaternion types in clifford algebras
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element.
Dmitry S Shirokov
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Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories [PDF]
, 2016 By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them.
Cheng, Tao, Huang, Hua-Lin, Yang, Yuping
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Clifford-Valued Shearlet Transforms on Cl(P,Q)-Algebras
Journal of Mathematics, 2022 The shearlet transform is a promising and powerful time-frequency tool for analyzing nonstationary signals. In this article, we introduce a novel integral transform coined as the Clifford-valued shearlet transform on Cl(p,q) algebras which is designed to
Firdous A. Shah +2 more
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Topological preons from algebraic spinors
European Physical Journal C: Particles and Fields, 2021 It is demonstrated that many of the assumed rules that govern the structure of a previously proposed topological preon model, in which simple non-trivial braids consisting of three twisted ribbons are mapped to the first generation of leptons and quarks,
Niels G. Gresnigt
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Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras
Nonlinear Analysis, 2022 The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
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Journal of Pure and Applied Algebra, 2019 We introduce a generalization, called a skew Clifford algebra, of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew Clifford algebras, and determine which skew Clifford algebras can be homogenized to create Artin-Schelter regular ...
Cassidy, Thomas, Vancliff, Michaela
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Representations of orthogonal and symplectic Yangians
Nuclear Physics B, 2021 Extended Yangian algebras of orthogonal and symplectic types are defined by the Yang-Baxter RLL relation involving the fundamental R-matrix with so(n) or sp(2m) symmetry. We study representations of highest weight characterized by weight function ratios.
D. Karakhanyan, R. Kirschner
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