Ring of symmetric functions

structure on ring of symmetric functions

 

1. commutative algebra
2. cocommutative coalgebra
3. antipode involutions
4. symmetric bilinear form <,> algebra structure dual to coalgebra structure
5. partial order \geq
6. lots of bases

 

1,2,3 => commutative, cocommutative Hopf algebra, coordinate ring of a commutative group scheme

 

 

S\otimes \mathbb{Q} is UEA of a Lie algebra