Exponentiation and deformations of Lie-admissible algebras
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-
- Journal Information:
- Hadronic J.; (United States), Vol. 5:3; Conference: 1. international conference on non-potential interactions and their Lie-admissible treatment, Orleans, France, 5 Jan 1982
- Country of Publication:
- United States
- Language:
- English
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