The Grothendieck ring of linear representations of a finite category
type: Item
instance of: scholarly article
title: The Grothendieck ring of linear representations of a finite category
zbMATH Open document ID: 0705.18007
author: D. Tambara
published in: Hokkaido Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: Let \({\mathcal C}\) be a finite category and k a field of characteristic \(p>0\). Denote by \(G_ 0(k[{\mathcal C}])\) (resp. \(K_ 0(k[{\mathcal C}]))\) the Grothendieck group of the category of finite dimensional (resp. finite dimensional projective) k[\({\mathcal C}]\)-modules. The author examines the Cartan map \(K_ 0(k[{\mathcal C}])\to G_ 0(k[{\mathcal C}])\) to prove a linear version of \textit{T. Yoshida}'s result [Commutative algebra and combinatorics, US-Jap. Joint Semin., Kyoto/Jap. 1985, Adv. Stud. Pure Math. 11, 337-353 (1987; Zbl 0645.20004)].
Mathematics Subject Classification ID: 18F30
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 4156724
zbMATH Keywords: Burnside ring
zbMATH Keywords: finite category
zbMATH Keywords: linear representation
zbMATH Keywords: Grothendieck group
zbMATH Keywords: Cartan map
reviewed by: Marek Golasiński
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381517365
OpenAlex ID: W2025208156
DOI: 10.14492/HOKMJ/1381517365
description: scientific article; zbMATH DE number 4156724