Article (Scientific journals)
Maximal subalgebras of vector fields for equivariant quantizations
Boniver, Fabien; Mathonet, Pierre
2001In Journal of Mathematical Physics, 42 (2), p. 582-589
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Keywords :
Maximal subalgebra; Polynomial vector field; Irreducible filtered algebra
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Boniver, Fabien
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Language :
English
Title :
Maximal subalgebras of vector fields for equivariant quantizations
Publication date :
February 2001
Journal title :
Journal of Mathematical Physics
ISSN :
0022-2488
eISSN :
1089-7658
Publisher :
American Institute of Physics, Melville, United States - New York
Volume :
42
Issue :
2
Pages :
582-589
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 16 May 2011

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