Automorphisms of the Koszul homology of a local ring

This work concerns the Koszul complex \(K\) of a commutative noetherian local ring \(R\), with its natural structure as differential graded \(R\)-algebra. It is proved that under diverse conditions, involving the multiplicative structure of \(H(K)\), any dg \(R\)-algebra automorphism of \(K\) induces the identity map on \(H(K)\). In such cases, it is possible to define an action of the automorphism group of \(R\) on \(H(K)\). On the other hand, numerous rings are described for which \(K\) has automorphisms that do not induce the identity on \(H(K)\). For any \(R\), it is shown that the group of automorphisms of \(H(K)\) induced by automorphisms of \(K\) is abelian.