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Approximation of the centre of unstables algebras using the nilpotent filtration

Abstract

In a precedent article, we computed the set C(K) of central elements of an unstable algebra K over the Steenrod algebra, in the sense of Dwyer and Wilkerson, when K is noetherian and nil_1-closed. For K noetherian and k a positive integer, we define C_k(K), the set of so-called central elements of K away from Nil_k in such a way that, for K nil k-closed, C(K) = C_k(K). The sets C_k(K) are a decreasing filtration, and we describe the obstruction for an element in C_k(K) to be in C_k+1(K). Since, for K noetherian, K is always nil k-closed for k big enough, this gives us a way to compute the set of central elements of K.
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hal-04107005 , version 1 (25-05-2023)

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Ouriel Bloede. Approximation of the centre of unstables algebras using the nilpotent filtration. 2023. ⟨hal-04107005⟩
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