Cartan matrices and Brauer's k(B)-Conjecture V

authored by

Cesare G. Ardito, Benjamin Sambale

Abstract

We prove Brauer's -Conjecture for the 3-blocks with abelian defect groups of rank at most 5 and for all 3-blocks of defect at most 4. For this purpose we develop a computer algorithm to construct isotypies based on a method of Usami and Puig. This leads further to some previously unknown perfect isometries for the 5-blocks of defect 2. We also investigate basic sets which are compatible under the action of the inertial group.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Manchester

Type

Article

Journal

Journal of Algebra

Volume

606

Pages

670-699

No. of pages

30

ISSN

0021-8693

Publication date

15.09.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.48550/arXiv.1911.10710 (Access: Open)
https://doi.org/10.1016/j.jalgebra.2022.04.035 (Access: Closed)