Recoupling Lie algebra and universal ω -algebra

We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω -algebra defined in this paper. ω -algebra is a generalization of algebra that goes beyond no...

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Bibliographic Details
Published in:Journal of mathematical physics 2004-10, Vol.45 (10), p.3859-3877
Main Author: Joyce, William P.
Format: Article
Language:English
Subjects:
Algebra
Theorems
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Summary:We formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation. This gives a generalization of graded Lie algebra. Underlying this is the new notion of an ω -algebra defined in this paper. ω -algebra is a generalization of algebra that goes beyond nonassociativity. We construct the universal enveloping ω -algebra of recoupling Lie algebras and prove a generalized Poincaré–Birkhoff–Witt theorem. As an example we consider the algebras over an arbitrary recoupling of Z n graded Heisenberg Lie algebra. Finally we uncover the usual coalgebra structure of a universal envelope and substantiate its Hopf structure.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1789281