Clifford Algebras
An Example of Clifford Algebras Calculations with GiNaC
... This example of Clifford algebras calculations uses GiNaC library [1], which includes a support for generic Clifford algebra starting from version 1.3.0. Both symbolic and numeric calculation are ...
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Three Clifford Algebras for Four Kinds of Interactions
... Since the geometric algebra of the physical space is isomorphic to the complex linear space of 2 2 × matric- es (Pauli algebra) the linear spaces of complex functions have invaded quantum physics. Nevertheless this iso- ...
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Clifford algebras and geometry of entanglement
... For the single qubit case, both pure and mixed states are discussed explicitly in terms of the Clifford algebra description along with the `mixedness' of a single qubit state, and the Ri[r] ...
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Explicit isomorphisms of real Clifford algebras
... By applying the above isomorphisms recursively, it is possible to get isomorphisms of Clifford algebras, but to apply these isomorphisms, we need some further isomorphisms among the vario[r] ...
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Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains
... Monogenic extension theorem of complex Cli ff ord algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of H ¨older continuous functions. ...
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Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces
... Sommen eds., Advances in Analysis and Geometry, New Developments Using Clifford Algebras, ISBN 3-7643-6661-3, Series Trends in Mathematics, Birkhauser Basel, 2004.. Transmission problems[r] ...
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Some Applications of Clifford Algebra in Geometry
... concrete Clifford algebra. Further development of the theory of Clifford algebras is associated with a number of famous mathematicians and physicists: ...that Clifford algebra is a unified ...
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Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups
... a group-like structure for B, called a bi-gyrogroup [34]. The use of Clifford algebras that may improve our understanding of bi-gyrogroups is found in [12]. Clearly, the notion of bi-gyrogroups extends the ...
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A Note on the Representation of Clifford Algebra
... K. Clifford in 1878[1], which combines length concept of Hamilton’s quaternion(1843, [2]) and Grassmann’s exterior algebra(1844, ...on Clifford algebra. Further devel- opment of the theory of ...
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Geometry of the Standard Model of Quantum Physics
... A quantum wave equation generalizing the Dirac wave equation has been proposed to explain the experimental results of the standard model of quantum physics. It does not require the second quantification nor the very te- ...
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Leopardi
... and Clifford algebras [10], and are presented here for completeness, since they are used ...of Clifford algebras [9] contains more background ...
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Algebra of Finite-Valued Functions: Classification of Functions and Subalgebras, Essential and Fictitious Subalgebras
... Algebras are not essentially maximal if they contain all functions that preserve relations with three centers. Each such algebra is a union of three algebras. Two of these algebras contain 512 ...
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The generalized path algebras over standardly stratified algebras
... ∆ = {∆(1), · · · , ∆(n)}. We denote by F(Θ) the full subcategory of ModΛ consisting of modules which have a filtration with factors in Θ, where ModΛ denotes the category of f.g. left modules over Λ and Θ is a set of ...
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FURTHER RESULTS OF NEUTROSOPHIC SUBALGEBRAS IN BCK=BCI-ALGEBRAS BASED ON NEUTROSOPHIC POINTS
... include Algebras re- lated to logic (BCK, BCI, BCC-algebras, Hilbert algebras, and implication algebras), soft algebraic structures, Algebraic Hyperstructures, Theory of derivations in ...
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Boundaries and equivariant products in unbounded Kasparov theory
... on Clifford multiplication by the inward unit normal on a manifold with boundary), we can construct a boundary Hilbert space with a representation of A/J ⊗ b C l 1 , as well as a symmetric operator on the boundary ...
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Fundamental hoop-algebras
... In this paper, we investigate some results on hoop algebras and hyper hoop-algebras. We construct a hoop and a hyper hoop on any countable set. Then using the notion of the fundamental relation we define ...
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On Characterizing Nilpotent Lie algebras by their Multipliers
... lie algebras is to use the dimension of the multiplier of ...those algebras whose multipliers have dimension close to the maximum, we call this invariant ...the algebras for values of t(L) and use ...
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ON INVERSE CATEGORIES AND TRANSFER IN COHOMOLOGY
... Proof of 1.1. We have already noted in 4.2 that kC is a direct product of matrix algebras over finite group algebras. In order to prove the statement on the symmetrising form, we need to follow the canonical ...
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The E8 geometry from a Clifford perspective
... via the so-called McKay correspondence [20], which in fact applies to all other binary polyhedral groups and the affine Lie algebras of ADE-type (cf. Fig. 3): firstly, we can define a graph by assigning a node to ...
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Derivations on QS- algebras
... derivations in BCI -algebras. They investigated some of its properties, defined a d -derivations ideal and gave conditions for an ideal to be d-derivations. Later, Abujabal and Al-Shehri [5], defined a left ...
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