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. ^[1]

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Table of Contents

1. 9 relations: Cambridge University Press, Character (mathematics), Cyclic group, Finite group, Group ring, Mathematics, Modular representation theory, Morita equivalence, Tree (graph theory).

Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

See Brauer tree and Cambridge University Press

Character (mathematics)

In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers).

See Brauer tree and Character (mathematics)

Cyclic group

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently \Zn or Zn, not to be confused with the commutative ring of p-adic numbers), that is generated by a single element.

See Brauer tree and Cyclic group

Finite group

In abstract algebra, a finite group is a group whose underlying set is finite. Brauer tree and finite group are finite groups.

See Brauer tree and Finite group

Group ring

In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group.

See Brauer tree and Group ring

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Brauer tree and Mathematics

Modular representation theory

Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number.

See Brauer tree and Modular representation theory

Morita equivalence

In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties.

See Brauer tree and Morita equivalence

Tree (graph theory)

In graph theory, a tree is an undirected graph in which any two vertices are connected by path, or equivalently a connected acyclic undirected graph.

See Brauer tree and Tree (graph theory)

References

[1] https://en.wikipedia.org/wiki/Brauer_tree

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