Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, 22D05, Article, non-abelian locally compact topological groups, 43A60, connected simple Lie group, Semisimple Lie groups and their representations, 510.mathematics, General properties and structure of locally compact groups, Structure of topological semigroups, idempotents, semitopological compactifications, weakly almost periodic, 22E30, semisimple Lie groups