semisimple

9.3

Having simple parts and no complex parts inside

adjective
/ˌsɛmɪˈsɪmpəl/

Specialized

: semisimple

When studying algebra, it is essential to recognize that semisimple modules can be decomposed into simpler components.
semisimple group

Examples

The main idea, common for all papers of this series, is that we first develop a representation theory for a solvable subgroup of the semisimple group, namely, for the Iwasawa group, and then extend it to the whole semisimple group.

Academic text (2018)
For example, in the class of real forms of semisimple Lie groups, this is the case only for the groups of real rank 1 except the symplectic groups; that is, only for those groups that do not have Kazhdan's property (for which the identity representation is isolated in the Fell topology in the space of irreducible unitary representations).

Academic text (2018)
Of course, the main interest was in semisimple groups; their study from this viewpoint was initiated in 2.

Academic text (2018)
The main idea, common for all papers of this series, is that we first develop a representation theory for a solvable subgroup of the semisimple group, namely, for the Iwasawa group, and then extend it to the whole semisimple group.

Academic text (2018)
We do not know whether Iwasawa groups of rank greater than one have special unitary representations. But anyway, these special representations cannot be extended to special unitary representations of the whole semisimple group.

Academic text (2018)
The study of these groups is not yet complete; however, one should turn to cases that do not fall into the framework of the existing schemes. Namely, what should one do with representations of groups of currents with values in O(p, q), U(p, q) for q > 1 and Sp(p, q), as well as in other real forms of semisimple groups?

Academic text (2018)
In mathematics, a semisimple group is composed entirely of simple groups and has no nontrivial normal subgroups.
The concept of being semisimple helps simplify the classification of certain algebraic structures.

Antonyms

complicated

∞ 5.4

Difficult to understand or deal with because it has many connected parts

complex

668 5.6

Not simple because it has many connected parts

Surface Forms

semisimple positive

Morphology

semisimple = simple (semi-transparent) = semi + simple

The word clearly combines 'semi-' with 'simple', but in mathematics the resulting meaning is a specialized technical term rather than the literal idea of being half simple.

Etymology

Semisimple combines semi- meaning 'half' or 'partly' and simple meaning 'not complex' or 'single'. So a semisimple object in math is like something made of simple parts or 'partly simple', which helps you remember it is built from simple pieces and does not have complicated inner parts.