noun
Meaning 1
A non-associative (not necessarily associative) algebra, A, over some field, together with a nondegenerate quadratic form, N, such that N(xy) = N(x)N(y) for all x, y ∈ A.
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
Examples
- 1993, F. L. Zak (translator and original author), Simeon Ivanov (editor), Tangents and Secants of Algebraic Varieties, American Mathematical Society, page 11, More precisely, Xn⊂PN is a Severi variety if and only if PN=P(J), where J is the Jordan algebra of Hermitian (3 × 3)-matrices over a composition algebra A, and X corresponds to the cone of Hermitian matrices of rank <1 (in that case SX corresponds to the cone of Hermitian matrices with vanishing determinant; cf. Theorem 4.8). In other words, X is a Severi variety if and only if X is the “Veronese surface” over one of the composition algebras over the field K (Theorem 4.9).
- 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 150, At least in the split cases, this is a construction that depends on two unital composition algebras, since the Jordan algebra involved consists of the 3 x 3-hermitian matrices over a unital composition algebra.
Meaning relationships
Synonyms: none provided
Antonyms: none provided