Coxeter Groups: Classification Theorem & Order of F_4

Related lectures (31)

Page 1 of 4

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Explores the properties of simple roots and reflections in Coxeter groups, emphasizing uniqueness and linear independence.

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.

Explores group homomorphisms, constructing isomorphisms between groups using generators and relations.

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Explores Coxeter elements, numbers, and planes in Coxeter groups with illustrative examples.

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.