Central Extensions of Lie Groups Preserving a Differential Form

Diez T, Janssens B, Neeb KH, Vizman C (2021)

Publication Type: Journal article

Publication year: 2021

Journal

International Mathematics Research Notices Oxford University Press (OUP): Policy H - Oxford Open Option A

Book Volume: 2021

Pages Range: 3794-3821

Journal Issue: 5

DOI: 10.1093/imrn/rnaa085

Abstract

Let M be a manifold with a closed, integral (k + 1)-form omega, and let G be a Frechet-Lie group acting on (M, omega). As a generalization of the Kostant-Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of g by R, indexed by Hk-1(M, R)*. We show that the image of Hk-1(M, Z) in Hk-1(M, R)* corresponds to a lattice of Lie algebra extensions that integrate to smooth central extensions of G by the circle group T. The idea is to represent a class in Hk-1(M, Z) by a weighted submanifold (S, beta), where beta is a closed, integral form on S. We use transgression of differential characters from S and M to the mapping space C-infinity (S, M) and apply the Kostant-Souriau construction on C 8 (S, M).

Authors with CRIS profile

Karl Hermann Neeb Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)

Involved external institutions

Max-Planck-Institut für Mathematik (MPIM) DE Germany (DE) Delft University of Technology (TU Delft) NL Netherlands (NL) West University Timisoara (WUT) RO Romania (RO)

How to cite

APA:

Diez, T., Janssens, B., Neeb, K.H., & Vizman, C. (2021). Central Extensions of Lie Groups Preserving a Differential Form. International Mathematics Research Notices, 2021(5), 3794-3821. https://doi.org/10.1093/imrn/rnaa085

MLA:

Diez, Tobias, et al. "Central Extensions of Lie Groups Preserving a Differential Form." International Mathematics Research Notices 2021.5 (2021): 3794-3821.

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