Brauer tree

In mathematics, in the theory of finite groups, a Brauer tree is a tree that encodes the characters of a block with cyclic defect group of a finite group. In fact, the trees encode the group algebra up to Morita equivalence. Such algebras coming from Brauer trees are called Brauer tree algebras. (Feit 1984) described the possibilities for Brauer trees.

References

• Feit, Walter (1984), "Possible Brauer trees", Illinois Journal of Mathematics 28 (1): 43–56, doi:10.1215/ijm/1256046152, ISSN 0019-2082, https://projecteuclid.org/euclid.ijm/1256046152 
• Hiss, G.; Lux, K. (1989), Brauer trees of sporadic groups, Oxford Science Publications, The Clarendon Press Oxford University Press, ISBN 978-0-19-853381-8, https://archive.org/details/brauertreesofspo0000hiss 
• Alperin, J.L. (1986), Local representation theory. Modular representations as an introduction to local representation theory of finite groups, Cambridge Studies in Advanced Mathematics, 11, Cambridge etc.: Cambridge University Press, ISBN 0-521-44926-X