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...

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

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

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

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...

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)...

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

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...

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...

{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...

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

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...

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...

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...

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...

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...

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...

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

types of algebraic structures are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures...

diagonal elements then these matrices form an exceptional (Grassmann) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups (F4...