Division Algebras, Clifford Algebras, Periodicity
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DOI: 10.1007/s00006-018-0820-8
Abstract: The dimensions 2, 8 and 24 play significant roles in lattice theory. In Clifford algebra theory there are well-known periodicities of the first two of these dimensions. Using novel representations of the purely Euclidean Clifford… read more here.
Keywords: periodicity; clifford; clifford algebras; division algebras ... See more keywords
Clifford Algebras as Twisted Group Algebras and the Arf Invariant
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DOI: 10.1007/s00006-018-0862-y
Abstract: Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit… read more here.
Keywords: algebras twisted; arf invariant; group algebras; twisted group ... See more keywords
Spinor Modules of Clifford Algebras in Classes $$N_{2k-1}$$N2k-1 and $$\Omega _{2k-1}$$Ω2k-1 are Determined by Irreducible Nonlinear Characters of Corresponding Salingaros Vee Groups
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DOI: 10.1007/s00006-018-0867-6
Abstract: Clifford algebras $$C \ell _{2,0}$$Cℓ2,0 and $$C \ell _{1,1}$$Cℓ1,1 are isomorphic simple algebras whose Salingaros vee groups belong to a class $$N_1$$N1. The algebras are isomorphic to the quotient algebra $$\mathbb {R}[D_8]/\mathcal {J}$$R[D8]/J of the… read more here.
Keywords: classes n2k; salingaros vee; spinor modules; clifford algebras ... See more keywords
Clifford Algebras, Multipartite Systems and Gauge Theory Gravity
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DOI: 10.1007/s00006-018-0917-0
Abstract: In this paper we present a multipartite formulation of gauge theory gravity based on the formalism of space–time algebra for gravitation developed by Lasenby and Doran (Philos Trans R Soc Lond A 582:356–487, 1998). We… read more here.
Keywords: multipartite systems; theory gravity; algebras multipartite; clifford algebras ... See more keywords
Construction of Multivector Inverse for Clifford Algebras Over $$2m+1$$2m+1-Dimensional Vector Spaces from Multivector Inverse for Clifford Algebras Over 2m-Dimensional Vector Spaces
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DOI: 10.1007/s00006-019-0942-7
Abstract: Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space $$\mathbb {R}^{p',q'}$$Rp′,q′, $$n'=p'+q'=2m$$n′=p′+q′=2m, we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension… read more here.
Keywords: vector spaces; multivector inverse; clifford algebras; dimensional vector ... See more keywords
Characteristic Polynomials in Clifford Algebras and in More General Algebras
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DOI: 10.1007/s00006-019-0944-5
Abstract: This article combines two independent theories: firstly, the algorithm of Faddeev–Leverrier which calculates characteristic polynomials of matrices; secondly, the Descent Theory which, in particular, lets many properties of matrix algebras descend down to Azumaya algebras,… read more here.
Keywords: characteristic polynomials; algebras characteristic; polynomials clifford; algebras general ... See more keywords
Classification of Extended Clifford Algebras
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DOI: 10.3103/s1066369x18110038
Abstract: Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford… read more here.
Keywords: extended clifford; clifford; clifford algebras; classification extended ... See more keywords
On Pauli’s Theorem in Clifford Algebras
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DOI: 10.3103/s1066369x19110033
Abstract: We study Pauli’s theorem in Clifford algebras. We offer an algorithm for constructing the Pauli operator and show that the problem of constructing the Pauli operator is connected with that of zero divisors in Clifford… read more here.
Keywords: pauli theorem; clifford algebras; theorem clifford;