QUOTIENT RINGS OF HF2 ∧ HF2

Agnès Beaudry, Michael A. Hill, Tyler Lawson, Xiaolin Danny Shi, Mingcong Zeng

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study modules over the commutative ring spectrum HF2 ∧ HF2, whose coefficient groups are quotients of the dual Steenrod algebra by collections of the Milnor generators. We show that very few of these quotients admit algebra structures, but those that do can be constructed simply: killing a generator ξk in the category of associative algebras freely kills the higher generators ξk+n. Using new information about the conjugation operation in the dual Steenrod algebra, we also consider quotients by families of Milnor generators and their conjugates. This allows us to produce a family of associative HF2 ∧ HF2-algebras whose coefficient rings are finite-dimensional and exhibit unexpected duality features. We then use these algebras to give detailed computations of the homotopy groups of several modules over this ring spectrum.

Original languageEnglish (US)
Pages (from-to)8949-8988
Number of pages40
JournalTransactions of the American Mathematical Society
Volume374
Issue number12
DOIs
StatePublished - 2021
Externally publishedYes

Bibliographical note

Funding Information:
Received by the editors April 7, 2021, and, in revised form, June 4, 2021. 2020 Mathematics Subject Classification. Primary 55N20, 55S05. This material is based upon work supported by the National Science Foundation under Grant No. DMS-1906227 and DMS-1811189.

Publisher Copyright:
© 2021 American Mathematical Society. All rights reserved.

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