In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle...

→ A which may or may not be associative. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidean space equipped...

In algebra, a noncommutative Jordan algebra is an algebra, usually over a field of characteristic not 2, such that the four operations of left and right...

type. All the algebraic and geometric structures associated with the symmetric space can be expressed naturally in terms of the Jordan algebra. The other...

called a homotope, of a unital Jordan algebra is a new Jordan algebra defined by a given element of the Jordan algebra. The mutation has a unit if and...

In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of...

In mathematics, quadratic Jordan algebras are a generalization of Jordan algebras introduced by Kevin McCrimmon (1966). The fundamental identities of...

classification of simple Jordan algebras. A Hurwitz algebra or composition algebra is a finite-dimensional not necessarily associative algebra A with identity...

In mathematics, Jordan operator algebras are real or complex Jordan algebras with the compatible structure of a Banach space. When the coefficients are...

introduced Jordan algebras in an effort to formalize quantum field theory; the algebras have since found numerous applications within mathematics. Jordan joined...

In algebra, the Kantor–Koecher–Tits construction is a method of constructing a Lie algebra from a Jordan algebra, introduced by Jacques Tits (1962), Kantor (1964)...

Hurwitz algebra is isomorphic to the original. A homotope of a Bernstein algebra by an element of non-zero weight is again a Bernstein algebra. A Jordan algebra...

{u, {v, w}}. In particular, any Lie algebra defines a Lie triple system and any Jordan algebra defines a Jordan triple system. They are important in...

mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra; read as "star-algebra") is a mathematical structure consisting of...

an algebraic structure over a field related to a Jordan algebra. The concept was introduced by Springer (1973) to develop a theory of Jordan algebras using...

division algebra A (i.e., R, C, H or O) there is a Jordan algebra, J3(A), of 3 × 3 A-Hermitian matrices. For any pair (A, B) of such division algebras, one...

In mathematics, specifically linear algebra, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley, expresses a linear operator...

algebra of a locally compact group Heyting algebra Hopf algebra Hurwitz algebra Hypercomplex algebra Incidence algebra Iwahori–Hecke algebra Jordan algebra...

Baer ring, Rickart ring Lie ring, Lie algebra Ideal (Lie algebra) Jordan algebra Differential algebra Banach algebra Examples Rational number, Real number...

mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure...

abstract algebra, a structurable algebra is a certain kind of unital involutive non-associative algebra over a field. For example, all Jordan algebras are...

form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras, which culminated in...

Jordan algebras in a similar way. The Jordan algebra J(m − 1) in the last row is the spin factor (which is the vector space Rm−1 ⊕ R, with a Jordan algebra...

domain. It can be described in terms of a Jordan pair or hermitian Jordan triple system. This Jordan algebra structure can be used to reconstruct the dual...

In mathematics, an isotopy from a possibly non-associative algebra A to another is a triple of bijective linear maps (a, b, c) such that if xy = z then...

Jordan frame may refer to: Jordan and Einstein frames, arising in the theory of relativity Jordan frame (Jordan algebra), complete sets of pairwise orthogonal...

representation of Lie algebra E 6 {\displaystyle \mathrm {E_{6}} } . The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint...

finite-dimensional division algebras over number fields and as the developer of Albert algebras, which are also known as exceptional Jordan algebras. A first generation...

linear algebra, a Jordan normal form, also known as a Jordan canonical form, is an upper triangular matrix of a particular form called a Jordan matrix...

Mutation (Jordan algebra), an operation on Jordan algebras that creates different Jordan algebras Mutation of a seed, in the theory of cluster algebras Apophony...