Editing Lie group decomposition (section)

{{onesource|date=September 2009}}
In [[mathematics]], '''Lie group decompositions''' are used to analyse the structure of [[Lie group]]s and associated objects, by showing how they are built up out of [[subgroup]]s. They are essential technical tools in the [[representation theory]] of Lie groups and [[Lie algebra]]s; they can also be used to study the [[algebraic topology]] of such groups and associated [[homogeneous space]]s. Since the use of Lie group methods became one of the standard techniques in twentieth century mathematics, many phenomena can now be referred back to decompositions.

The same ideas are often applied to Lie groups, Lie algebras, [[algebraic group]]s and [[p-adic number]] analogues, making it harder to summarise the facts into a unified theory.