Projective unitary representations of infinite-dimensional Lie groups
| Autor: | Bas Janssens, Karl-Hermann Neeb |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
infinite-dimensional Lie groups 17B65 FOS: Physical sciences unitary representation theory 01 natural sciences Unitary state 17B67 17B68 22E60 17B15 17B56 17B65 17B67 17B68 22E45 22E60 22E65 22E66 22E67 0103 physical sciences Lie algebra FOS: Mathematics Point (geometry) 22E66 22E45 22E67 Representation Theory (math.RT) 0101 mathematics 22E65 Mathematical Physics Smooth structure Mathematics 010102 general mathematics Regular polygon Lie group Mathematical Physics (math-ph) Extension (predicate logic) 17B15 17B56 infinite-dimensional Lie algebras Unitary representation 010307 mathematical physics Mathematics - Representation Theory |
| Zdroj: | Kyoto J. Math. 59, no. 2 (2019), 293-341 |
| ISSN: | 2156-2261 |
| Popis: | For an infinite dimensional Lie group $G$ modelled on a locally convex Lie algebra $\mathfrak{g}$, we prove that every smooth projective unitary representation of $G$ corresponds to a smooth linear unitary representation of a Lie group extension $G^{\sharp}$ of $G$. (The main point is the smooth structure on $G^{\sharp}$.) For infinite dimensional Lie groups $G$ which are 1-connected, regular, and modelled on a barrelled Lie algebra $\mathfrak{g}$, we characterize the unitary $\mathfrak{g}$-representations which integrate to $G$. Combining these results, we give a precise formulation of the correspondence between smooth projective unitary representations of $G$, smooth linear unitary representations of $G^{\sharp}$, and the appropriate unitary representations of its Lie algebra $\mathfrak{g}^{\sharp}$. Comment: 47 pages |
| Databáze: | OpenAIRE |
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