# Contents

## Idea

For $A$ an ordinary associative algebra, its tangent complex is its module of derivations.

For $A$ a dg-algebra, its tangent complex is the essentially the value of the derived functor of the derivations-assigning functor on $A$. This is closely related to the automorphism ∞-Lie algebra of $A$.

## References

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