On the universal enveloping algebra ofsl 2(C)
Copyright policy ) M. C. Prati;
On the universal enveloping algebra ofsl 2(C)
For the universal enveloping algebraU ofsl 2(C), we consider the decompositionU≌Z⊗H. HereZ is the center ofU, generated by the (unique) Casimir operator Δ, andH is thesl 2-module $$ \pi _0 \oplus \pi _1 \oplus \pi _2 ... $$ , where πk is the irreducible representation ofsl 2 with dimension2k+1. We choose a basis inU according to this decomposition and we study the Lie algebra structure ofU over the ringZ.
- Scuola Normale Superiore Italy
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