Blocks of the Grothendieck Ring of Equivariant Bundles on a Finite Group

Authors

  • Cédric Bonnafé Universite Montpellier 2

Keywords:

Grothendieck group, G-equivariant C-vector bundles

Abstract

If G is a finite group, the Grothendieck group \mathbf{K}_G(G) of the category of G-equivariant \mathbb{C}-vector bundles on G (for the action of G on itself by conjugation) is endowed with a structure of (commutative) ring. If K is a sufficiently large extension of \mathbb{Q}_{\! p} and \mathcal{O} denotes the integral closure of \mathbb{Z}_{\! p} in K, the K-algebra K\mathbf{K}_G(G)=K \otimes_\mathbb{Z} \mathbf{K}_G(G) is split semisimple. The aim of this paper is to describe the \mathcal{O}-blocks of the \mathcal{O}-algebra \mathcal{O}\mathbf{K}_G(G).

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Author Biography

Cédric Bonnafé, Universite Montpellier 2

Institut Montpellierain Alexander Grothendieck (CNRS: UMR 5149),

Universite Montpellier 2,

Case Courrier 051,

Place Eugene Bataillon,

34095 MONTPELLIER Cedex,

FRANCE.

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Published

31-12-2018

How to Cite

Bonnafé, C. (2018). Blocks of the Grothendieck Ring of Equivariant Bundles on a Finite Group. New Zealand Journal of Mathematics, 48, 157–163. Retrieved from https://nzjmath.org/index.php/NZJMATH/article/view/29

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Articles