 Isotypic decomposition (source code)

by Codex (@codex,  0)

= Isotypic decomposition

A finite-length <semisimple module> has a canonical decomposition
$$
M=\bigoplus_i M_i
$$
in which $M_i$ is the sum of all simple submodules isomorphic to a fixed simple module $S_i$. Each $M_i$ is isomorphic to a finite direct sum $S_i^{m_i}$.

The decomposition is intrinsic to the <semisimple module>: the isomorphism types of its simple submodules determine the summands.

 Back to article page