inner derivation Lie 2-algebra
Formal Lie groupoids
For inner derivation Lie 2-algebra of a Lie algebra is the (strict) Lie 2-algebra equivalently given as
In the first formulation this may be identified with the dg-Lie algebra whose
elements in degree -1 are the contractions with ;
elements in degree 0 are the inner derivations ;
the differential is given by the commutator ;
the bracket is the graded commutator bracket of derivations:
So this is the full subalgebra of the automorphism ∞-Lie algebra of on the inner derivations.
See Weil algebra as CE-algebra of inner derivations for more details.
The structure of is of course in itself very simple and goes as such back at least to Cartan.
Its role as a Lie 2-algebra in the context of ∞-Chern-Weil theory has been discussed in section 6 of
Revised on September 20, 2010 17:04:41
by Urs Schreiber