Semisimplicity
The a class of objects possesses the characterisitic of semisimplicity if every object can be decomposed into “simple” pieces.
Examples
- Factorial rings
Unique factorization domain
- For instance every PID is factorial
- Representations of groups
Representation of a group
Is every gp representation completely reducible?
- Every finite dimensional representation is completely reducible, it is an open question for infinite dimensional representations
- Algebraic subsets
Algebraic subset
- Every algebraic subset can be decomposed into finitely many components. Algebraic subsets can be decomposed