In mathematical finite group theory, a Brauer tree is a planar tree

Tree (graph theory)

In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree...

 that encodes the characters of a block with cyclic defect group

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity...

 of a finite group G. In fact, the trees encode the group algebra up to Morita equivalence

Morita equivalence

In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958.- Motivation :...

. Such algebras coming from Brauer trees are called Brauer tree algebras.

described the possibilities for Brauer trees.