Tor Algebra Structures for Compressed Rings
Keller VandeBogert – University of South Carolina
A differential graded (DG) algebra is an algebra equipped with a differential satisfying the graded Leibniz (product) rule. The existence of associative DG structures on minimal free resolutions implies many desirable properties of the module being resolved. Moreover, any such DG structure induces an algebra structure on so-called Tor modules. In this talk, we will examine the Tor algebra structure of certain classes of compressed rings. In particular, we will encounter a new class of counterexamples to a conjecture of Avramov and show that there exist ideals defining rings of arbitrarily large type whose Tor algebra has class G.