Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Γεροντογιάννης Δημήτριος-Μιχαήλ
Supervisors info:
Ιάκωβος Ανδρουλιδάκης Επίκ. Καθηγητής
Original Title:
Παραμόρφωση στον κανονικό κώνο και το εφαπτόμενο ομαδοειδές
Translated title:
Deformation to the normal cone and the tangent groupoid
Summary:
Quantization is the process of transition from a classical system to a quantum
system. Strict (deformation) quantization is an approach to quantization in the
C*-algebraic framework which can be seen as a generalisation to Weyl
quantization of the canonical Poisson structure on . The underlying geometry of
Weyl quantization is that of a family of translations on . Therefore one thinks
of groupoids which in addition lead to the strict quantization on
non-homogeneous spaces. A unifying whole to many strict quantizations is
obtained by the strict quantization of the fibrewise linear Poisson structure
on the dual Lie algebroid [LaRa]. This construction is closely related to the
integrability of the Lie algebroid. Our main tool is the generalisation of
Connes tangent groupoid [Con1] to arbitrary Lie groupoids [HS], where this idea
originates from the deformation to the normal cone in the area of algebraic
geometry.
Keywords:
Tubular neighbourhood theorem, Deformation to the normal cone, Tangent groupoid, Strict quantization
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