Generalization of Hurwitz theorem and flexible Lie-admissible algebras

Conference · Sat Dec 01 04:00:00 EST 1979 · Hadronic J.; (United States)

OSTI ID:6554515

Okubo, S

Any algebra P satisfying the composition law (xy, xy) = (x, x) (y, y) and the invariance condition (xy, z) = (x,yz) has been completely classified when the underlying field F is algebraically closed and of characteristic not equal to 2, and not equal to 3. The dimension of the algebra is limited to 1, 2, 4, and 8. It is shown that the usual Hurwitz theorem can be derivable from this classification as a special case. Also, various classifications and constructions of flexible Lie-admissible algebras are discussed. The importance of quasi-classical Lie algebras for general classification of simple flexible Lie-admissible algebras has been emphasized and utilized. Several products which behave covariantly under quasi-equivalent transformation have been discussed. Also, a notion of super-flexible law has been introduced with some results.

• Research Organization: Univ. of Rochester, NY
• OSTI ID: 6554515
• Report Number(s): CONF-7908175-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 3:1
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
CLASSIFICATION
LIE GROUPS
MATHEMATICS
SYMMETRY GROUPS
TRANSFORMATIONS