CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations . Please improve this article by introducing more precise citations. (March 2013) 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. The algebras produced by this process are known as Cayley–Dickson algebras . They are useful composition algebras frequently applied in mathematical physics . The Cayley–Dickson construction defines a new algebra based on the direct sum of an algebra with itself, with multiplication defined in a specific way and an involution known as conju...