Algebras of operations in K-theory
Francis Clarke, Martin Crossley, Sarah Whitehouse
TL;DR
This paper explicitly describes the algebraic structure of degree zero operations in connective and periodic p-local complex K-theory, including formulas for their product and coproduct, and discusses their non-Noetherian nature.
Contribution
It provides explicit descriptions and formulas for the algebras of operations in p-local complex K-theory, including Adams summand and real K-theory, highlighting their algebraic properties.
Findings
Operations are expressed as infinite linear combinations of Adams operations.
The rings of operations are shown to be non-Noetherian.
Formulas for product and coproduct structures are provided.
Abstract
We describe explicitly the algebras of degree zero operations in connective and periodic p-local complex K-theory. Operations are written uniquely in terms of certain infinite linear combinations of Adams operations, and we give formulas for the product and coproduct structure maps. It is shown that these rings of operations are not Noetherian. Versions of the results are provided for the Adams summand and for real K-theory.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models