Alternativkörper und quadratische systeme

Zorn, Max

doi:10.1007/bf02940661

Cited by 56 publications

(29 citation statements)

References 4 publications

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“…Therefore, octonion algebra cannot be isomorphic to associative matrix algebra [11]. To overcome this problem, Zorn de…ned vector matrix representation for split octonion algebra [2]. After the de…nition of vector matrix representation this representation is altered for real octonion algebra [7].…”

Section: Vector Matrix Representation Of Octonion Algebramentioning

confidence: 99%

Vector matrix representation of octonions and their geometry

HALICI

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: Vector Matrix Representation Of Octonion Algebramentioning

confidence: 99%

Vector matrix representation of octonions and their geometry

HALICI

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…of Zorn vector matrices over k, i.e., of 2 × 2 matrices with diagonal entries in k and off-diagonal ones in column space k 3 over k. The normalization chosen here is due to Zorn [24] and turns out to be the most convenient for our subsequent computations. Accordingly, we define…”

Section: 2mentioning

confidence: 99%

Inner derivations of alternative algebras over commutative rings

Loos

Petersson

Racine

2008

ANT

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Erhard Neher zum 60. Geburtstag gewidmetWe define Lie multiplication derivations of an arbitrary non-associative algebra A over any commutative ring and, following an approach due to K. McCrimmon, describe them completely if A is alternative. Using this description, we propose a new definition of inner derivations for alternative algebras, among which Schafer's standard derivations and McCrimmon's associator derivations occupy a special place, the latter being particularly useful to resolve difficulties in characteristic 3. We also show that octonion algebras over any commutative ring have only associator derivations.

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“…Zorn [7] gave a representation of the octonions [8] in terms of 2 × 2 matrices M , whose diagonal elements are scalars and whose off-diagonal elements are 3-dimensional vectors:…”

Section: Zorn's Representation Of Octonionsmentioning

confidence: 99%

“…and invoked a peculiar multiplication rule for these matrices [7]. With slight modification of the rule adopted by Humphreys [10] p. 105 our rule is:…”

Section: Zorn's Representation Of Octonionsmentioning

confidence: 99%

Matrix representation of octonions and generalizations

Daboul

Delbourgo

1999

Journal of Mathematical Physics

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We define a special matrix multiplication among a special subset of 2N × 2N matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative non-associative and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley-Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts.

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Alternativkörper und quadratische systeme

Cited by 56 publications

References 4 publications

Vector matrix representation of octonions and their geometry

Vector matrix representation of octonions and their geometry

Inner derivations of alternative algebras over commutative rings

Matrix representation of octonions and generalizations

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