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Polynomial extensions of the Weyl C*-algebra

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Date
2010
Publisher city
Paris
Publisher
Université Paris-Dauphine
Link to item file
http://hal.archives-ouvertes.fr/hal-00483172/fr/
Dewey
Algèbre
Sujet
Heseinberg group; Galilei Algebra; Galilei group; Heisenberg algebra
URI
https://basepub.dauphine.fr/handle/123456789/4272
Collections
  • CEREMADE : Publications
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Author
Dhahri, Ameur
Accardi, Luigi
Type
Document de travail / Working paper
Item number of pages
32
Abstract (EN)
We introduce higher order (polynomial) extensions of the unique (up to isomorphisms) non trivial central extension of the Heisenberg algebra. Using the boson representation of the latter, we construct the corresponding polynomial analogue of the Weyl C*-algebra and use this result to deduce the explicit form of the composition law of the associated generalization of the 1-dimensional Heisenberg group. These results are used to calculate the vacuum characteristic func- tions as well as the moments of the observables in the Galilei algebra. The continuous extensions of these objects gives a new type of second quantization which even in the quadratic case is quite different from the quadratic Fock functor.

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