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   Articles with "division algebras" as a keyword



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Division Algebras, Clifford Algebras, Periodicity

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recommendations! Published in 2018 at "Advances in Applied Clifford Algebras"

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
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On eight-dimensional unital division algebras over finite fields

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recommendations! Published in 2017 at "Communications in Algebra"

DOI: 10.1080/00927872.2017.1288235

Abstract: ABSTRACT The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry. read more here.

Keywords: finite fields; algebras finite; division algebras; unital division ... See more keywords
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Valuations on Algebraic Division Algebras

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recommendations! Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2017.1339065

Abstract: ABSTRACT Let D be a division algebra algebraic over its center F. Given a (Krull) valuation v on F, it is shown that v extends to a valuation on D if and only if for… read more here.

Keywords: division; valuations algebraic; division algebras; algebraic division ... See more keywords
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Duplication methods for embeddings of real division algebras

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recommendations! Published in 2020 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498822500633

Abstract: We introduce two groups of duplication processes that extend the well known Cayley–Dickson process. The first one allows to embed every 4-dimensional (4D) real unital algebra ???? into an 8D real unit... read more here.

Keywords: duplication; methods embeddings; real division; division algebras ... See more keywords