Classification of 6-dimensional real Manin triples
Quantum Algebra
2007-05-23 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We present a complete list of 6-dimensional Manin triples or, equivalently, of 3-dimensional Lie bialgebras. We start from the well known classification of 3-dimensional real Lie algebras and assume the canonical bilinear form on the 6-dimensional Drinfeld double. Then we solve the Jacobi identities for the dual algebras. Finally we find mutually non-isomorphic Manin triples. The complete list consists of 78 classes of Manin triples, or 44 Lie bialgebras if one considers dual bialgebras equivalent.
Cite
@article{arxiv.math/0202209,
title = {Classification of 6-dimensional real Manin triples},
author = {L. Hlavaty and L. Snobl},
journal= {arXiv preprint arXiv:math/0202209},
year = {2007}
}
Comments
21 pages, added references and details of computations