The Use of Quantum Algebras in Quantum Gravity

Details The Use of Quantum Algebras in Quantum Gravity The Use of Quantum Algebras in Quantum Gravity

1999-11-24

arxiv.org/abs/gr-qc/9911094v1

EconfC990712:304-309,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

6 pages, LaTeX. Contribution to proceedings of III Int. Conference "Symmetry in Nonlinear Mathematical Physics" (Kiev, 12-18 J

Scientific paper

After a brief survey of the appearance of quantum algebras in diverse contexts of quantum gravity, we demonstrate that the particular deformed algebras, which arise within the approach of J.Nelson and T.Regge to 2+1 anti-de Sitter quantum gravity (for space surface of genus g) and which are basic for generating the algebras of independent quantum observables, are in fact isomorphic to the nonstandard q-deformed analogues U'_q(so_n) (introduced in 1991) of Lie algebras of the orthogonal groups SO(n), with n linked to g as n=2g+2.

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