2021/04/01 by Srikanth B. Iyengar, Iyengar, Srikanth B., Henrik Rüping +3
Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 13D02 #Secondary 13A50
paper · pdf · doi:10.48550/arxiv.2104.00726
openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.