Anchor

An anchor is the Bundle Map $\rho$ from a Vector Bundle $A$ to the Tangent Bundle TB satisfying

1. $[\rho(X),\rho(Y)]=\rho([X,Y])$ and

2. $[X,\phi Y]=\phi[X, Y]+(\rho(X)\cdot \phi)Y,$

where $X$ and $Y$ are smooth sections of $A$, $\phi$ is a smooth function of $B$, and the bracket is the ``Jacobi-Lie bracket'' of a Vector Field.

See also Lie Algebroid

References

Weinstein, A. ``Groupoids: Unifying Internal and External Symmetry.'' Not. Amer. Math. Soc. 43, 744-752, 1996.