Abstract
A differential graded (DG) free algebra is a connected cochain DG algebra such that its underlying graded algebra is
We prove that the differential structures on DG free algebras are in one to one correspondence with the set of crisscross ordered n-tuples of n × n matrices. We also give a criterion to judge whether two DG free algebras are isomorphic. As an application, we consider the case of n = 2. Based on the isomorphism classification, we compute the cohomology graded algebras of non-trivial DG free algebras with two generators, and show that all those non-trivial DG free algebras are Koszul and Calabi-Yau.
2010 Mathematics Subject Classification: