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This article is cited in 1 scientific paper (total in 1 paper)
Differential geometry and quantization on a locally compact group
S. S. Akbarov
Abstract:
For an arbitrary locally compact group $G$, we describe the structure of the Lie
algebra $\chi(G)$ of vector fields, the exterior algebra $\Lambda(G)$ of differential forms, and the Poisson algebra of symbols on $G$ polynomial with respect to the momenta. A continuous left-invariant $qp$-quantizaton is constructed, giving rise to a one-to-one correspondence between symbols and differential operators on $G$. It is demonstrated that neither of the other two classical quantizations, namely, the $pq$ and Weyl quantizations, can be constructed on an infinite group $G$ if the same properties are to be retained.
Received: 10.11.1993
Citation:
S. S. Akbarov, “Differential geometry and quantization on a locally compact group”, Izv. RAN. Ser. Mat., 59:2 (1995), 47–62; Izv. Math., 59:2 (1995), 271–286
Linking options:
https://www.mathnet.ru/eng/im11https://doi.org/10.1070/IM1995v059n02ABEH000011 https://www.mathnet.ru/eng/im/v59/i2/p47
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Abstract page: | 362 | Russian version PDF: | 107 | English version PDF: | 9 | References: | 26 | First page: | 1 |
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