In mathematics, "semisimple" refers to a structure that can be broken down into simpler components that do not interact with each other. For example, in the context of algebra, a semisimple algebra can be expressed as a direct sum of simple algebras, which are the most basic building blocks. This property makes semisimple structures easier to analyze and understand. In the realm of group theory, a semisimple group is one that can be decomposed into a product of simple groups. These groups have no nontrivial normal subgroups, meaning they cannot be broken down further. Semisimplicity is an important concept in various areas of mathematics, including representation theory and Lie algebras.