Phrase guide

Hurwitz algebra

noun · 1 senses · updated from the 2026-07-25 local source snapshot

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Pronunciation

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1

noun

Meaning 1

Any one of the unital composition algebras identified by Hurwitz's theorem (on composition algebras) as solutions to the Hurwitz problem.

Definition source: English Wiktionary via Wiktextract

Topics: algebra, mathematics, sciences

Examples

  • 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]).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after German mathematician Adolf Hurwitz (1859–1919); see also Hurwitz problem, Hurwitz's theorem.