We give natural descriptions of the homology and cohomology algebras of regular quotient ring spectra of even E∞-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.
We apply recent work of A. Lazarev which develops an obstruction theory for the existence of R-algebra structures on Rmodules, where R is a commutative S-algebra. We show that certain M U -modules have such A ∞ structures. Our results are often simpler to state for the related BP -modules under the currently unproved assumption that BP is a commutative Salgebra. Part of our motivation is to clarify the algebra involved in Lazarev's work and to generalize it to other important cases. We also make explicit the fact that BP admits an M U -algebra structure as do E(n) and E(n), in the latter case rederiving and strengthening older results of U. Würgler and the first author.The first author would like to thank the Mathematisches Institut, Universität Bern for providing a stimulating environment in which much of this work was carried out. We would also like to thank Christian Ausoni for helpful comments.
Abstract. In this paper, we show that the p-adic K-theory of a connected p-compact is the ring of invariants of the Weyl group action on the K-theory of a maximal torus. We apply this result to show that a connected finite loop space admits a maximal torus if and only if its complex K-theory is λ-isomorphic to the K-theory of some BG, where G is a compact connected Lie group.Mathematics Subject Classification (1991). Primary 55P35, 55R35, 55N15.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.