Modular representation theory of cyclic group:Z3

This article describes the modular representation theory of cyclic group:Z3, the cyclic group of order three, i.e., the linear representation theory of the group in characteristic three, which means the linear representation theory over field:F3 and its extensions.

For the linear representation theory in other characteristics, see linear representation theory of cyclic group:Z3.

Irreducible representations
There is a unique irreducible representation: the trivial representation, which sends all elements of the group to the matrix $$( 1 )$$. This is a general feature common to all representations of a group of prime power order in a field of characteristic equal to the prime.

Indecomposable representations
There are (up to equivalence of linear representations) three indecomposable representations: