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The tensor product theorem for &∇tilde;-nilpotence and the dimension of unstable modules

Published online by Cambridge University Press:  18 May 2001

GEOFFREY M. L. POWELL
GEOFFREY M. L. POWELL
Affiliation:
Laboratoire Analyse, Géométrie et Applications, UMR 7539, Institut Galilée, Université Paris 13, 93430 Villetaneuse, France. e-mail: [email protected]
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Abstract

Let [Fscr ] be the category of functors from the category of finite-dimensional [ ]2-vector spaces to [ ]2-vector spaces. The concept of &∇tilde;-nilpotence in the category [Fscr ] is used to define a ‘dimension’ for the category of analytic functors which has good properties. In particular, the paper shows that the tensor product F [otimes ] G of analytic functors which are respectively &∇tilde;s and &∇tilde;t nilpotent is &∇tilde;s+t − 1-nilpotent.

The notion of &∇tilde;-nilpotence is extended to define a dimension in the category of unstable modules over the mod 2 Steenrod algebra, which is shown to coincide with the transcendence degree of an unstable Noetherian algebra over the Steenrod algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 3 , May 2001 , pp. 427 - 439
Copyright
2001 Cambridge Philosophical Society

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