Maximal subalgebras of vector fields for equivariant quantizations

Details Maximal subalgebras of vector fields for equivariant quantizations Maximal subalgebras of vector fields for equivariant quantizations

2000-09-28

arxiv.org/abs/math/0009239v2

Mathematics

Differential Geometry

11 pages, to appear in J. Math. Phys. --- ref. added and typos fixed

Scientific paper

10.1063/1.1332782

The elaboration of new quantization methods has recently developed the interest in the study of subalgebras of the Lie algebra of polynomial vector fields over a Euclidean space. In this framework, these subalgebras define maximal equivariance conditions that one can impose on a linear bijection between observables that are polynomial in the momenta and differential operators.Here, we determine which finite dimensional graded Lie subalgebras are maximal. In order to characterize these, we make use of results of Guillemin, Singer and Sternberg and Kobayashi and Nagano.

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