Lie-admissible algebras with specified automorphism groups

Conference · Sun Feb 01 04:00:00 EST 1981 · Hadronic J.; (United States)

OSTI ID:6934945

Oehmke, R H ^[1]; Oehmke, J F

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1. Univ. of Iowa, Iowa City

Let a be an algebra with products indicated by uv. To each algebra a we associate an algebra a/sup -/ which is the same vector space as a but whose product is defined by (u,v) = uv - vu. If a/sup -/ is a Lie algebra, we say that a is a Lie-admissible algebra. The class of all Lie-admissible algebras is a very broad class in the sense that individual members appear to have very disparate underlying structures. In order to gain greater insight into this structure, we have constructed a number of examples lying in a proper subclass of the class of Lie-admissible algebras. Since our interest in the general problem has been motivated by physical considerations, we have let this same interest determine the type of examples we sought. We have confined our attention to the class of algebra a for which a/sup -/ is su(3,F). This choice not only kept the underlying computations tractable but also kept a high potential for possible applications. All of the examples we have given admit a group of automorphisms induced by conjugation by 3 x 3 upper triangular matrices whose diagonal elements are ones. We show that these examples form a basis for all such algebras. The derivation of these results is highly computational. While it would be inappropriate to record here each step of these computations, we have attempted to give some indication of our computational process and some indications of the less obvious directions we might have taken.

• OSTI ID: 6934945
• Report Number(s): CONF-8008162-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 4:2
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRAIC FIELD THEORY
AXIOMATIC FIELD THEORY
FIELD THEORIES
LIE GROUPS
QUANTUM FIELD THEORY
SYMMETRY GROUPS