✦ LIBER ✦
Isomorphisms of Finite Invariant for Enveloping Algebras, Semi-simple Case
✍ Scribed by Philippe Caldero
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 240 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
✦ Synopsis
Let g be a finite dimensional semi-simple Lie algebra, U(g) its enveloping algebra, and H a finite subgroup of Aut U(g). Let A be the invariant algebra U H . In this article, we prove that the Lie algebra g is given (up to an isomorphism) by the algebra A. If we impose that H is a finite subgroup of the adjoint group of g acting on the enveloping algebra U(g), then the algebra A gives a unique group algebra C[H]. If g=sl 2 , then the group H can be recovered from A.