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...

takes any algebra with involution to another algebra with involution of twice the dimension.: 45  Hurwitz's theorem (composition algebras) states that...

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, 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...

{\displaystyle x=4} ). Algebra over a set Algebra tile Algebraic combinatorics C*-algebra Composition algebra Computer algebra Exterior algebra F-algebra F-coalgebra...

single function Composition (combinatorics), a way of writing a positive integer as a sum of positive integers Composition algebra, an algebra over a field...

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...

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

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...

series of exercises prove that a composition algebra is always an alternative algebra. Algebra over a field Maltsev algebra Zorn ring Schafer (1995) p. 27...

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...

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...

{\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...

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...

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

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...

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

quadratic form of a bicomplex number indicates that these numbers form a composition algebra. In fact, bicomplex numbers arise at the binarion level of the Cayley–Dickson...

{\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...

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

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

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

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

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...

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

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

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

overview, see Algebra. The bare word "algebra" may refer to: Elementary algebra Abstract algebra Algebra over a field In universal algebra, algebra has an axiomatic...

A non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative...