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Structurable algebras and models of compact simple Kantor triple systems defined on tensor products of composition algebras
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2005 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 33, no 2, 549-558 p.Article in journal (Refereed) Published
Abstract [en]

Let (A,(-)) be a structurable algebra. Then the opposite algebra (A(op),(-)) is structurable, and we show that the triple system B-A(op) (x, y, z) := V-x,y(op)(z) = x(yz) + z(yx) - y(xz), x, y, z is an element of A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A = A(1) circle times A(2) denotes tensor products of composition algebras, ((-)) is the standard conjugation, and () denotes a certain pseudoconjugation on A, we show that the triple systems B-A1 circle times A2(op) (x, y, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dimA(1), dimA(2)) not equal (2, 2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras.

Place, publisher, year, edition, pages
2005. Vol. 33, no 2, 549-558 p.
Keyword [en]
composition algebras, Kantor triple systems, structurable algebras
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-38032DOI: 10.1081/AGB-200047437ISI: 000227594700013Scopus ID: 2-s2.0-27944491961OAI: oai:DiVA.org:kth-38032DiVA: diva2:435764
Note
QC 20110819Available from: 2011-08-19 Created: 2011-08-19 Last updated: 2017-12-08Bibliographically approved

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