Nilpotence and generation in the stable module category

David J. Benson, Jon F. Carlson*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Nilpotence has been studied in stable homotopy theory and algebraic geometry. We study the corresponding notion in modular representation theory of finite groups, and apply the discussion to the study of ghosts, and generation of the stable module category. In particular, we show that for a finitely generated kG-module M, the tensor M-generation number and the tensor M-ghost number are both equal to the degree of tensor nilpotence of a certain map associated with M.

Original languageEnglish
Pages (from-to)3566-3584
Number of pages19
JournalJournal of Pure and Applied Algebra
Volume222
Issue number11
Early online date8 Feb 2018
DOIs
Publication statusPublished - 30 Nov 2018

Fingerprint

Tensor
Module
Stable Homotopy
Modular Representations
Homotopy Theory
Algebraic Geometry
Representation Theory
Finitely Generated
Finite Group

Keywords

  • Nilpotence
  • homotopy
  • algebraic geometry

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Nilpotence and generation in the stable module category. / Benson, David J.; Carlson, Jon F.

In: Journal of Pure and Applied Algebra, Vol. 222, No. 11, 30.11.2018, p. 3566-3584.

Research output: Contribution to journalArticle

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