KMLIEGROUPS

Infinite-dimensional Lie theory and Kac-Moody groups

Coordinatore	FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG    more  Organization address address: SCHLOSSPLATZ 4 city: ERLANGEN postcode: 91054 contact info Titolo: Ms. Nome: Franziska Cognome: Müller Email: send email Telefono: +49 9131 85 26474 Fax: +49 9131 85 26239
Nazionalità Coordinatore	Germany [DE]
Totale costo	168˙794 €
EC contributo	168˙794 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2013-IEF
Funding Scheme	MC-IEF
Anno di inizio	2014
Periodo (anno-mese-giorno)	2014-10-01   -   2016-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG  Organization address address: SCHLOSSPLATZ 4 city: ERLANGEN postcode: 91054 contact info Titolo: Ms. Nome: Franziska Cognome: Müller Email: send email Telefono: +49 9131 85 26474 Fax: +49 9131 85 26239	DE (ERLANGEN)	coordinator	168˙794.40

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 Obiettivo del progetto (Objective)

'Lie theory was created at the end of the 19th century, and rapidly became a central chapter of contemporary mathematics. Finite-dimensional Lie groups and Lie algebras were extensively studied for more than a century, and are well understood. In attempting to generalise the finite-dimensional objects, one can roughly distinguish two general approaches, one 'analytic' (keeping the smooth manifold structure of Lie groups) and the other “algebraic” (which is best represented by the algebraic constructions of Kac-Moody groups).

Although intensively studied, Kac–Moody groups and Lie groups beyond the affine case remain mysterious to a large extent, and many questions concerning their structure remain open. In my Ph.-D. thesis, I established several structure results concerning topological Kac–Moody groups of indefinite type, and part of this research project carries on this study further. The main goal of this research project is to get a better understanding of Kac–Moody groups beyond the affine case, from both the analytic and algebraic approaches, and to try to construct “concrete realisations” of these groups (at least for hyperbolic types), by studying the unitary representations of their Lie algebra. More precisely, my method would be to try to construct certain “concrete” representations of a distinguished class of Lie algebras that include all symmetrisable Kac–Moody algebras; it should then be possible to construct “concrete realisations” of the corresponding groups by integrating these representations, hopefully allowing for an in-depth study of these groups.

This research project would allow me to significantly broaden and diversify my mathematical knowledge and experience, as I would study Kac-Moody groups and algebras from a wholly different perspective (the 'analytic' one) and investigate its applications to theoretical physics, thus placing my research in an interdisciplinary context.'