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Showing 1 to 9 of 9 for “"clifford algebras"”.
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Formalizing Clifford algebras and related constructions in the Lean theorem prover
… of the latter, in the more abstract setting of Clifford algebras. It does so via the theorem proving language “Lean”, which is seeing increasing adoption in mathematics departments. The focus is much broader than simply formalizing Clifford algebras; Lean has an expansive and monolithic library …
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Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… complex) noncommutative and nonassociative algebras $\bbO_{p,q}$ (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. Introduced by Morier-Genoud and Ovsienko, these …
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The combinatorics of adinkras
… to study representations of supersymmetry algebras. Besides having inherent interest for physicists, the study of adinkras has already shown nontrivial connections with coding theory and Clifford algebras. Furthermore, adinkras offer many easy-to-state and accessible mathematical problems …
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Applications of the Pauli algebra and other geometric algebras.
… are developed by presenting them as geometrical (Clifford) algebras. Rotations are examined using both quaternions and the Pauli algebra, and in particular, algorithms that are used in three-dimensional simulations and video games are formulated in the Pauli algebra. Relativity is presented using …
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Genera via Deformation Theory and Supersymmetric Mechanics
… This involves investigating supertraces on Weyl-Clifford algebras and deformations of symplectic supermanifolds.
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New relativistic solutions for classical charges in an electromagnetic field.
… Lorentz transformations in the framework of the Clifford algebra Cℓ3. The paravector subspace of the algebra, a four-dimensional space defined to contain scalars and spatial vectors, shares the metric structure of Minkowski spacetime. With the flexible advantage of Clifford algebras in vector …
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Gravity, spinors and gauge-natural bundles
… basic results that we need on Lie groups, Lie algebras and Lie group actions on manifolds. Finally, Appendix D consists of a short introduction to Clifford algebras and spinors.
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On the structure of geometries with spinor-type connexion
… is based upon properties of so-called tangent Clifford algebras. The tangent Clifford algebra to a space-time manifold at a certain point is the quotient space of the algebra of covariant tensors at the point by a certain two-sided ideal, and is uniquely defined once the metric structure of the …
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A Geometric Model for Real and Complex Differential K-theory
… spectra defined by Behrens using spaces of Clifford module extensions. After writing representative differential forms for the universal Pontryagin and Chern characters we transgress these forms to all the spaces of the spectra and use them to define an abelian group structure on maps up to …