In mathematics, a composition algebra A over a field K is a not necessarily associative algebra over K together with a nondegenerate quadratic form N...

possibilities. Such algebras, sometimes called Hurwitz algebras, are examples of composition algebras. The theory of composition algebras has subsequently...

examples are useful composition algebras frequently applied in mathematical physics. The Cayley–Dickson construction defines a new algebra as a Cartesian product...

In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative. That is, one must have x...

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...

generalized to form algebras of dimension 2n over a field F with involution. The square function z2 is the "norm" of the composition algebra C {\displaystyle...

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

hypercomplexity: Hurwitz's theorem says finite-dimensional real composition algebras are the reals R {\displaystyle \mathbb {R} } , the complexes C {\displaystyle...

In mathematics, an octonion algebra or Cayley algebra over a field F is a composition algebra over F that has dimension 8 over F. In other words, it is...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

{\displaystyle N(wz)=N(w)N(z).} This composition of N over the algebra product makes (D, +, ×, *) a composition algebra. A similar algebra based on ⁠ R 2 {\displaystyle...

= 1. Banach algebra Composition algebra Division algebra Gelfand–Mazur theorem Hurwitz's theorem (composition algebras) "Normed Algebra". Encyclopaedia...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems...

studied by Susumu Okubo. Okubo algebras are composition algebras, flexible algebras (A(BA) = (AB)A), Lie admissible algebras, and power associative, but...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process...

algebras is given by the square root of the composition algebra norm. In general the norm of a composition algebra may be a quadratic form that is not definite...

quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a matrix algebra by extending...

In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins...

operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings...

phy.olemiss.edu. Retrieved 2021-07-18. The Wikibook Associative Composition Algebra has a page on the topic of: Poincaré group Wu-Ki Tung (1985). Group...

Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard bold...

mathematics, and more specifically in abstract algebra, a rng (or non-unital ring or pseudo-ring) is an algebraic structure satisfying the same properties as...

f. Such chains have the algebraic structure of a monoid, called a transformation monoid or (much more seldom) a composition monoid. In general, transformation...

divisor. The algebra of biquaternions forms a composition algebra and can be constructed from bicomplex numbers. See § As a composition algebra below. Note...

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented...

{\displaystyle N(z)} in composition algebras does not share the usual properties of a norm since null vectors are allowed. A composition algebra ( A , ∗ , N ) {\displaystyle...