Journal of the Aust Math Soc (Ser A)

Jacqui Ramagge
Mathematics Department
University of Newcastle
NSW 2308
Australia
e-mail: jacqui@maths.newcastle.edu.au
and
Wayne W. Wheeler
Department of Mathematics
University of Georgia
Athens, GA 30602
USA
e-mail: www@alpha.math.uga.edu

If P is a partially ordered set and R is a commutative ring, then a certain differential graded R-algebra $A_{\bullet}(P)$ is defined from the order relation on P. The algebra $A_{\bullet}(\emptyset)$ corresponding to the empty poset is always contained in $A_{\bullet}(P)$ so that $A_{\bullet}(P)$ can be regarded as an $A_{\bullet}(\emptyset)$ -algebra. The main result of this paper shows that if R is an integral domain and P and P' are finite posets such that $A_{\bullet}(P)\cong A_{\bullet}(P')$ as differential graded $A_{\bullet}(\emptyset)$ -algebras, then P and P' are isomorphic.

Posets and differential graded algebras

Abstract: