Definition of Semisimple. Meaning of Semisimple. Synonyms of Semisimple

- In mathematics, specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation...
- a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring that is a semisimple module...
- reducibility says a finite-dimensional representation of a semisimple compact Lie group is semisimple. A square matrix (in other words a linear operator T :...
- In ring theory, a branch of mathematics, a semisimple algebra is an ****ociative artinian algebra over a field which has trivial Jacobson radical (only...
- In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any...
- Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general than a semisimple ring, but...
- be completely reducible (or semisimple) if it is isomorphic to a direct sum of irreducible representations (cf. semisimple module). If V is finite-dimensional...
- symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive. Claude Chevalley showed that the classification...
- context: A semisimple element in the endomorphism ring of a vector space is a semisimple operator. In a semisimple Lie algebra, an element is semisimple if its...
- semisimple if every T-invariant subspace has a complementary T-invariant subspace. If T is a semisimple linear operator on V, then V is a semisimple representation...