Homology, Homotopy and Applications

Volume 26 (2024)

Number 1

Unstable algebras over an operad II

Pages: 37 – 67

DOI: https://dx.doi.org/10.4310/HHA.2024.v26.n1.a4


Sacha Ikonicoff (Department of Mathematics and Statistics, STEM Complex, University of Ottawa, Ontario, Canada)


$\def\P\{\mathcal{P}}$We work over the finite field $\mathbb{F}_q$. We introduce a notion of unstable $\P$-algebra over an operad $\P$. We show that the unstable $\P$-algebra freely generated by an unstable module is itself a free $\P$-algebra under suitable conditions. We introduce a family of ‘$q$-level’ operads which allows us to identify unstable modules studied by Brown–Gitler, Miller and Carlsson in terms of free unstable $q$-level algebras.


Steenrod algebra, bialgebra, unstable module, operad

2010 Mathematics Subject Classification

17A30, 55S10

Copyright © 2024, Sacha Ikonicoff. Permission to copy for private use granted.

Received 10 January 2023

Received revised 27 February 2023

Accepted 28 February 2023

Published 21 February 2024