Details
| Original language | English |
|---|---|
| Pages (from-to) | 582-585 |
| Number of pages | 4 |
| Journal | Journal of algebra |
| Volume | 489 |
| Early online date | 9 Aug 2017 |
| Publication status | Published - 1 Nov 2017 |
| Externally published | Yes |
Abstract
Wada conjectured in 2007 that the largest eigenvalue of the Cartan matrix C of a block of a finite group is rational if and only if all eigenvalues of C are rational. We provide a counterexample to this conjecture and discuss related questions.
Keywords
- Cartan matrices of blocks, Eigenvalues, Rationality
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of algebra, Vol. 489, 01.11.2017, p. 582-585.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A counterexample to a conjecture of Wada
AU - Sambale, Benjamin
N1 - Funding information: I thank Thomas Breuer for some explanations about character tables in GAP. Moreover, I am grateful to Gabriel Navarro for getting me interested in counterexamples. This work is supported by the German Research Foundation (project SA 2864/1-1 ).
PY - 2017/11/1
Y1 - 2017/11/1
N2 - Wada conjectured in 2007 that the largest eigenvalue of the Cartan matrix C of a block of a finite group is rational if and only if all eigenvalues of C are rational. We provide a counterexample to this conjecture and discuss related questions.
AB - Wada conjectured in 2007 that the largest eigenvalue of the Cartan matrix C of a block of a finite group is rational if and only if all eigenvalues of C are rational. We provide a counterexample to this conjecture and discuss related questions.
KW - Cartan matrices of blocks
KW - Eigenvalues
KW - Rationality
UR - http://www.scopus.com/inward/record.url?scp=85027678786&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2017.08.002
DO - 10.1016/j.jalgebra.2017.08.002
M3 - Article
AN - SCOPUS:85027678786
VL - 489
SP - 582
EP - 585
JO - Journal of algebra
JF - Journal of algebra
SN - 0021-8693
ER -