Exponentiation and deformations of Lie-admissible algebras

Conference · Thu Apr 01 04:00:00 EST 1982 · Hadronic J.; (United States)

OSTI ID:6699332

Myung, H C

The exponential function is defined for a finite-dimensional real power-associative algebra with unit element. The application of the exponential function is focused on the power-associative (p,q)-mutation of a real or complex associative algebra. Explicit formulas are computed for the (p,q)-mutation of the real envelope of the spin 1 algebra and the Lie algebra so(3) of the rotation group, in light of earlier investigations of the spin 1/2. A slight variant of the mutated exponential is interpreted as a continuous function of the Lie algebra into some isotope of the corresponding linear Lie group. The second part of this paper is concerned with the representation and deformation of a Lie-admissible algebra. The second cohomology group of a Lie-admissible algebra is introduced as a generalization of those of associative and Lie algebras in the Hochschild and Chevalley-Eilenberg theory. Some elementary theory of algebraic deformation of Lie-admissible algebras is discussed in view of generalization of that of associative and Lie algebras. Lie-admissible deformations are also suggested by the representation of Lie-admissible algebras. Some explicit examples of Lie-admissible deformation are given in terms of the (p,q)-mutation of associative deformation of an associative algebra. Finally, we discuss Lie-admissible deformations of order one.

• Research Organization: Univ. of Northern Iowa, Cedar Falls
• OSTI ID: 6699332
• Report Number(s): CONF-820136-
• Conference Information: Journal Name: Hadronic J.; (United States) Journal Volume: 5:3
• Country of Publication: United States
• Language: English

Related Subjects

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