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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 47–62 (Mi izv11)  

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.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 271–286

Bibliographic databases:

MSC: 22E30
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

Citation in format AMSBIB
\Bibitem{Akb95}
\by S.~S.~Akbarov
\paper Differential geometry and quantization on a~locally compact group
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 47--62
\mathnet{http://mi.mathnet.ru/izv11}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1337158}
\zmath{https://zbmath.org/?q=an:0897.22014}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 271--286
\crossref{https://doi.org/10.1070/IM1995v059n02ABEH000011}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. S. Akbarov, “Construction of the cotangent bundle of a locally compact group”, Izv. Math., 59:3 (1995), 445–470  mathnet  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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