For an ordinary associative algebra, its tangent complex is its module of derivations.
For a dg-algebra, its tangent complex is the essentially the value of the derived functor of the derivations-assigning functor on . This is closely related to the automorphism ∞-Lie algebra of .
The concept goes back to
- M. Schlessinger, Jim Stasheff, The Lie algebra structure of tangent cohomology and deformation theory , J. Pure Appl. Algebra, 38(1985), 313–322.
The tangent complex of an algebra over an operad in chain complexes is discussed in section 8 of
- Jonathan Block, A. Lazarev, André-Quillen cohomology and rational homotopy of function spaces , Advances in mathematics, 193 (2005) (pdf)
Revised on March 17, 2011 22:10:59
by Urs Schreiber