Clifford algebras from quotient ring spectra

Abstract

We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E-infinity ring spectra. We show that the homology is a Clifford algebra with respect to a certain bilinear form naturally associated to the quotient ring spectrum F. To identify the cohomology algebra, we first determine the derivations of F and then prove that the cohomology is isomorphic to the exterior algebra on the module of derivations. We treat the example of the Morava K-theories in detail.

Final version (to appear). Changes: new paragraph in 1.1, amended Definition 2.14, new Remark 3.6, amended proof of Proposition 5.1 (reference problem eliminated), various minor changes