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The algebra of traces for conformal gravity in \(2+1\) dimensions. (English) Zbl 1176.81120

Summary: The Poisson bracket algebra for the traces of the integrated connection (gauge invariant quantities) of conformal gravity in \(2+1\) dimensions is explicitly constructed and turns out to be an infinite Lie algebra.

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
17B81 Applications of Lie (super)algebras to physics, etc.
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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References:

[1] Horne, J. H.; Witten, E., Phys. Rev. Lett., 62, 501 (1989)
[2] Nelson, J. E.; Regge, T., Nucl. Phys. B, 328, 190 (1989)
[3] Nelson, J. E.; Regge, T.; Zertuche, F., Nucl. Phys. B, 339, 516 (1990)
[4] Zertuche, F.; Urrutia, L. F., The Poincaré limit in 2+1 dimensional quantum De Sitter gravity (1990), preprint UNAM-ICN
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