Quadratic Jordan superalgebras

Authors
Citation
D. King, Quadratic Jordan superalgebras, COMM ALGEB, 29(1), 2001, pp. 375-401
Citations number
23
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
0092-7872 → ACNP
Volume
29
Issue
1
Year of publication
2001
Pages
375 - 401
Database
ISI
SICI code
0092-7872(2001)29:1<375:QJS>2.0.ZU;2-X
Abstract
This paper examines Kevin McCrimmon's proposed definition for a quadratic J ordan superalgebra meaningful over an arbitrary ring of scalars. Efim Zel'm anov has proposed two conditions that such a definition should satisfy: fir st, all the simple, finite-dimensional, linear Jordan superalgebras of char acteristic 0 in Kac' classification should have simple, quadratic Jordan su peralgebra analogs, and second, these should be essentially all the simple, finite-dimensional, quadratic Jordan superalgebras of characteristic 0. He re we verify the first condition. Specifically we study the quadratic super algebra analogues of full linear superalgebras, Hermitian superalgebras, Ka plansky's superalgebras, Kac's split 10-dimensional superalgebra, and super algebras of quadratic forms with base point.