Prequantization and extensions

• Grant number: 18/07297-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: July 01, 2018
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Agreement: 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)

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.