Octonion algebra and Split-octonion

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Octonion algebra and Split-octonion

Octonion algebra vs. Split-octonion

In mathematics, an octonion algebra or Cayley algebra over a field F is an algebraic structure which is an 8-dimensional composition algebra over F. In other words, it is a unital non-associative algebra A over F with a non-degenerate quadratic form N (called the norm form) such that for all x and y in A. The most well-known example of an octonion algebra is the classical octonions, which are an octonion algebra over R, the field of real numbers. In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers.

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (English: Papers from the Mathematical Seminar of the University of Hamburg) is a peer-reviewed mathematics journal published by Springer Science+Business Media.

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Academic Press

Academic Press is an academic book publisher.

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Alternative algebra

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.

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Cayley–Dickson construction

In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one.

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Composition algebra

In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Isotropic quadratic form

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Max August Zorn

Max August Zorn (June 6, 1906 – March 9, 1993) was a German mathematician.

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Moufang loop

In mathematics, a Moufang loop is a special kind of algebraic structure.

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Octonion

In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are three lower-dimensional normed division algebras over the reals: the real numbers R themselves, the complex numbers C, and the quaternions H. The octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension.

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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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