DG structure on the length 4 big from small construction.

The big from small construction was introduced by Kustin and Miller in [A. Kustin and M. Miller, Constructing big Gorenstein ideals from small ones, J. Algebra85 (1983) 303–322] and can be used to construct resolutions of tightly double linked Gorenstein ideals. In this paper, we expand on the DG-algebra techniques introduced in [A. Kustin, Use DG methods to build a matrix factorization, preprint (2019), arXiv:1905.11435] and construct a DG R -algebra structure on the length 4 big from small construction. The techniques employed involve the construction of a morphism from a Tate-like complex to an acyclic DG R -algebra exhibiting Poincaré duality. This induces homomorphisms which, after suitable modifications, satisfy a list of identities that end up perfectly encapsulating the required associativity and DG axioms of the desired product structure for the big from small construction. [ABSTRACT FROM AUTHOR]