Lie Group Decomposition
In mathematics, Lie group decompositions, named after Sophus Lie, are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of subgroups. They are essential technical tools in the representation theory of Lie groups and Lie algebras; they can also be used to study the algebraic topology of such groups and associated homogeneous spaces. 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 groups and p-adic number analogues, making it harder to summarise the facts into a unified theory.
Read more about Lie Group Decomposition: List of Decompositions
Famous quotes containing the words lie and/or group:
“The wolf also shall dwell with the lamb, and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them.”
—Bible: Hebrew Isaiah, 11:6.
“For me, as a beginning novelist, all other living writers form a control group for whom the world is a placebo.”
—Nicholson Baker (b. 1957)