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KMLIEGROUPS

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Infinite dimensional Lie theory and Kac Moody groups

"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 wel... ver más

30/09/2016

FAU

169K€

Presupuesto del proyecto: 169K€

Líder del proyecto

FRIEDRICHALEXANDERUNIVERSITAET ERLANGENNUERNB... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2016-09-30 No tenemos la información de la convocatoria

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Líder del proyecto

FRIEDRICHALEXANDERUNIVERSITAET ERLANGENNUERNB... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 169K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto "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."

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