Isomorphisms of twisted Hilbert loop algebras

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Marquis T, Neeb KH
Zeitschrift: Canadian Journal of Mathematics-Journal Canadien De Mathematiques
Verlag: University of Toronto Press
Jahr der Veröffentlichung: 2017
ISSN: 0008-414X


Abstract


The closest infinite dimensional relatives of compact Lie algebras are Hilbert-Lie algebras, i.e. real Hilbert spaces with a Lie algebra structure for which the scalar product is invariant. Locally affine Lie algebras (LALAs) correspond to double extensions of (twisted) loop algebras over simple Hilbert-Lie algebras k, also called affinisations of k. They possess a root space decomposition whose corresponding root system is a locally affine root system of one of the 7 families A(1)J, B(1)J, C(1)J, D(1)J, B(2)J, C(2)J and BC(2)J for some infinite set J. To each of these types corresponds a "minimal" affinisation of some simple Hilbert-Lie algebra k, which we call standard.

In this paper, we give for each affinisation g of a simple Hilbert-Lie algebra k an explicit isomorphism from g to one of the standard affinisations of k. The existence of such an isomorphism could also be derived from the classification of locally affine root systems, but for representation theoretic purposes it is crucial to obtain it explicitely as a deformation between two twists which is compatible with the root decompositions. We illustrate this by applying our isomorphism theorem to the study of positive energy highest weight representations of g.

In subsequent work, the present paper will be used to obtain a complete classification of the positive energy highest weight representations of affinisations of k.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Marquis, Timothée Dr.
Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)
Neeb, Karl-Hermann Prof. Dr.
Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)


Zitierweisen

APA:
Marquis, T., & Neeb, K.-H. (2017). Isomorphisms of twisted Hilbert loop algebras. Canadian Journal of Mathematics-Journal Canadien De Mathematiques. https://dx.doi.org/10.4153/CJM-2016-003-x

MLA:
Marquis, Timothée, and Karl-Hermann Neeb. "Isomorphisms of twisted Hilbert loop algebras." Canadian Journal of Mathematics-Journal Canadien De Mathematiques (2017).

BibTeX: 

Zuletzt aktualisiert 2019-29-01 um 13:08