Lie Bialgebra - Definition

Definition

More precisely, comultiplication on the algebra, is called the cocommutator, and must satisfy two properties. The dual

must be a Lie bracket on, and it must be a cocycle:

\delta = \left(
\operatorname{ad}_X \otimes 1 + 1 \otimes \operatorname{ad}_X
\right) \delta(Y) - \left(
\operatorname{ad}_Y \otimes 1 + 1 \otimes \operatorname{ad}_Y
\right) \delta(X)

where is the adjoint.

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