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Prequantization and extensions

Grant number: 18/07297-2
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): July 01, 2018
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Acordo de Cooperação: Coordination of Improvement of Higher Education Personnel (CAPES)
Principal Investigator:Igor Mencattini
Grantee:Pedro Henrique Carvalho Silva
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this project we will study some aspects of Lie theory and some of its interactions with symplectic geometry. In particular we will investigate under which assumptions a connected Lie group G acting on a connected symplectic manifold (M,É) via symplectomorphisms, admits a central extensions G2 acting as a group of symmetries of a pair (L,±) of a principal R/D-bundle, where D is a discrete subgroup of the reals, and ± is a connection one-form on L whose curvature is the pull-back of É via the canonical projection p : L ’ M. We will see how this problem is strictly related to the problem of pre-quantizing the classical phase-space (M, É) and to the problem of the existence of the central extension of the Lie group G integrating a central extension of the corresponding Lie algebra g. (AU)

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
SILVA, Pedro Henrique Carvalho. Central extensions and Symplectic Geometry. 2020. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.

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