Faster access than browser!
40 relations: Abelian group, Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Academic Press, Adolf Hurwitz, Algebra homomorphism, Algebra over a field, Algebraic group, Algebraic structure, Algebraically closed field, Alternative algebra, American Mathematical Society, Bioctonion, Cambridge University Press, Cayley–Dickson construction, Complex number, Composition algebra, Degeneracy (mathematics), Dimension (vector space), Division algebra, Dover Publications, Eponym, Field (mathematics), Finite field, G2 (mathematics), Galois cohomology, German language, Graduate Studies in Mathematics, Isotropic quadratic form, Leonard Eugene Dickson, Mathematics, Max August Zorn, Moufang loop, Octonion, Pfister form, Principal homogeneous space, Quadratic form, Quaternion algebra, Real number, Split-octonion, Springer Science+Business Media.
Abelian group
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
New!!: Octonion algebra and Abelian group · See more »
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.
New!!: Octonion algebra and Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg · See more »
Academic Press
Academic Press is an academic book publisher.
New!!: Octonion algebra and Academic Press · See more »
Adolf Hurwitz
Adolf Hurwitz (26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory.
New!!: Octonion algebra and Adolf Hurwitz · See more »
Algebra homomorphism
A homomorphism between two associative algebras, A and B, over a field (or commutative ring) K, is a function F\colon A\to B such that for all k in K and x, y in A,.
New!!: Octonion algebra and Algebra homomorphism · See more »
Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
New!!: Octonion algebra and Algebra over a field · See more »
Algebraic group
In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inversion operations are given by regular maps on the variety.
New!!: Octonion algebra and Algebraic group · See more »
Algebraic structure
In mathematics, and more specifically in abstract algebra, an algebraic structure on a set A (called carrier set or underlying set) is a collection of finitary operations on A; the set A with this structure is also called an algebra.
New!!: Octonion algebra and Algebraic structure · See more »
Algebraically closed field
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
New!!: Octonion algebra and Algebraically closed field · See more »
Alternative algebra
In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.
New!!: Octonion algebra and Alternative algebra · See more »
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
New!!: Octonion algebra and American Mathematical Society · See more »
Bioctonion
In mathematics, a bioctonion, or complex octonion, is a pair of biquaternions (p,q), p,q ∈. The product of two bioctonions is defined using biquaternion multiplication and the biconjugate p → p*: The bioctonion z.
New!!: Octonion algebra and Bioctonion · See more »
Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
New!!: Octonion algebra and Cambridge University Press · See more »
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.
New!!: Octonion algebra and Cayley–Dickson construction · See more »
Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
New!!: Octonion algebra and Complex number · See more »
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.
New!!: Octonion algebra and Composition algebra · See more »
Degeneracy (mathematics)
In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.
New!!: Octonion algebra and Degeneracy (mathematics) · See more »
Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
New!!: Octonion algebra and Dimension (vector space) · See more »
Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.
New!!: Octonion algebra and Division algebra · See more »
Dover Publications
Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward Cirker and his wife, Blanche.
New!!: Octonion algebra and Dover Publications · See more »
Eponym
An eponym is a person, place, or thing after whom or after which something is named, or believed to be named.
New!!: Octonion algebra and Eponym · See more »
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.
New!!: Octonion algebra and Field (mathematics) · See more »
Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
New!!: Octonion algebra and Finite field · See more »
G2 (mathematics)
In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak_2, as well as some algebraic groups.
New!!: Octonion algebra and G2 (mathematics) · See more »
Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups.
New!!: Octonion algebra and Galois cohomology · See more »
German language
German (Deutsch) is a West Germanic language that is mainly spoken in Central Europe.
New!!: Octonion algebra and German language · See more »
Graduate Studies in Mathematics
Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS).
New!!: Octonion algebra and Graduate Studies in Mathematics · See more »
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.
New!!: Octonion algebra and Isotropic quadratic form · See more »
Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician.
New!!: Octonion algebra and Leonard Eugene Dickson · See more »
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
New!!: Octonion algebra and Mathematics · See more »
Max August Zorn
Max August Zorn (June 6, 1906 – March 9, 1993) was a German mathematician.
New!!: Octonion algebra and Max August Zorn · See more »
Moufang loop
In mathematics, a Moufang loop is a special kind of algebraic structure.
New!!: Octonion algebra and Moufang loop · See more »
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.
New!!: Octonion algebra and Octonion · See more »
Pfister form
In mathematics, a Pfister form is a particular kind of quadratic form, introduced by Albrecht Pfister in 1965.
New!!: Octonion algebra and Pfister form · See more »
Principal homogeneous space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial.
New!!: Octonion algebra and Principal homogeneous space · See more »
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
New!!: Octonion algebra and Quadratic form · See more »
Quaternion algebra
In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes the matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, A \otimes_F K is isomorphic to the 2×2 matrix algebra over K. The notion of a quaternion algebra can be seen as a generalization of Hamilton's quaternions to an arbitrary base field.
New!!: Octonion algebra and Quaternion algebra · See more »
Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
New!!: Octonion algebra and Real number · See more »
Split-octonion
In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers.
New!!: Octonion algebra and Split-octonion · See more »
Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
New!!: Octonion algebra and Springer Science+Business Media · See more »
Redirects here:
Cayley algebra, Split octonion algebra.
References
[1] https://en.wikipedia.org/wiki/Octonion_algebra
