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  Gradient representations and affine structures in AEn

Kleinschmidt, A., & Nicolai, H. (2005). Gradient representations and affine structures in AEn. Classical and Quantum Gravity, 22, 4457-4487. doi:10.1088/0264-9381/22/21/004.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4F35-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4F37-8
Genre: Journal Article

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 Creators:
Kleinschmidt, Axel1, Author              
Nicolai, Hermann2, Author              
Affiliations:
1Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: We study the indefinite Kac-Moody algebras AE(n), arising in the reduction of Einstein's theory from (n+1) space-time dimensions to one (time) dimension, and their distinguished maximal regular subalgebras sl(n) and affine A_{n-2}^{(1)}. The interplay between these two subalgebras is used, for n=3, to determine the commutation relations of the `gradient generators' within AE(3). The low level truncation of the geodesic sigma-model over the coset space AE(n)/K(AE(n)) is shown to map to a suitably truncated version of the SL(n)/SO(n) non-linear sigma-model resulting from the reduction Einstein's equations in (n+1) dimensions to (1+1) dimensions. A further truncation to diagonal solutions can be exploited to define a one-to-one correspondence between such solutions, and null geodesic trajectories on the infinite-dimensional coset space H/K(H), where H is the (extended) Heisenberg group, and K(H) its maximal compact subgroup. We clarify the relation between H and the corresponding subgroup of the Geroch group.

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Language(s): eng - English
 Dates: 2005
 Publication Status: Published in print
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 Identifiers: eDoc: 222411
DOI: 10.1088/0264-9381/22/21/004
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Title: Classical and Quantum Gravity
Source Genre: Journal
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Pages: - Volume / Issue: 22 Sequence Number: - Start / End Page: 4457 - 4487 Identifier: ISSN: 0264-9381