Classification of 6-dimensional real Manin triples

Details Classification of 6-dimensional real Manin triples Classification of 6-dimensional real Manin triples

2002-02-21

arxiv.org/abs/math/0202209v2

Mathematics

Quantum Algebra

21 pages, added references and details of computations

Scientific paper

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.

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