Hurwitz algebra

English Etymology Named after German mathematician Adolf Hurwitz (1859–1919); see also en Hurwitz problem, en Hurwitz's theorem. Noun en algebra Any one of the unital composition algebras identified by Hurwitz's theorem (on composition algebras) as solutions to the Hurwitz problem. en 1995 Susumo Okubo Introduction to Octonion and Other Non-Associative Algebras in Physics https://books.google.com.au/books?id=Tr3qQugHUvQC&pg=PA40&dq=%22Hurwitz+algebra%22%7C%22Hurwitz+algebras%22&hl=en&sa=X&ved=0ahUKEwjjisO2ldjeAhVKgJAKHVUjCzMQ6AEIODAD#v=onepage&q=%22Hurwitz%20algebra%22%7C%22Hurwitz%20algebras%22&f=false 40 w:Cambridge University Press As we recall, a Hurwitz algebra is a composition algebra with unit element. en 1998 Max-Albert Knus; Alexander Merkurjev; Markus Rost; Jean-Pierre Tignol The Book of Involutions w:American Mathematical Society https://books.google.com.au/books?id=iNDTyyoaLMIC&pg=PA465&dq=%22Hurwitz+algebra%22%7C%22Hurwitz+algebras%22&hl=en&sa=X&ved=0ahUKEwjjisO2ldjeAhVKgJAKHVUjCzMQ6AEIKDAA#v=onepage&q=%22Hurwitz%20algebra%22%7C%22Hurwitz%20algebras%22&f=false 465 Observe that the unital composition algebra associated with by the construction given in the proof of Proposition (33.27) is the Hurwitz algebra if we set . 2006, Alberto Elduque, Chapter 12: A new look at Freudenthal's Magic Square, Lev Sabinin, Larissa Sbitneva, Ivan Shestakov (editors, Non-Associative Algebra and Its Applications, Taylor & Francis Group (Chapman & Hall/CRC), page 15, Unital composition algebras (or Hurwitz algebras) form a well-known class of algebras. Any Hurwitz algebra has a finite dimension equal to either 1, 2, 4, or 8. The two-dimensional Hurwitz algebras are the quadratic étale algebras over the ground field F, the four dimensional ones are the generalized quaternion algebras, and the eight dimensional Hurwitz algebras are called Cayley algebras, and are analog to the classical algebra of octonions (for a good survey of the latter, see [Bae02]). Hyponyms en Euclidean Hurwitz algebra Derived terms en para-Hurwitz algebra Translations unital composition algebra that is a solution to the Hurwitz problem See also en composition algebra Further reading Hurwitz's theorem (composition algebras) Definite quadratic form Clifford algebra en eponyms