Electronic Resource
Springer
Communications in mathematical physics
212 (2000), S. 535-556
ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: We classify realizations of the Lie algebras of the rotation O(3) and Euclid E(3) groups within the class of first-order differential operators in arbitrary finite dimensions. It is established that there are only two distinct realizations of the Lie algebra of the group O(3) which are inequivalent within the action of a diffeomorphism group. Using this result we describe a special subclass of realizations of the Euclid algebra which are called covariant ones by analogy to similar objects considered in classical representation theory. Furthermore, we give an exhaustive description of realizations of the Lie algebra of the group O(4) and construct covariant realizations of the Lie algebra of the generalized Euclid group E(4).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200000222
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