Year: 2007
Type: preprint
Abstract: With a nilpotent element in a semisimple Lie algebra g one associates a finitely generated associative algebra W called a W-algebra of finite type. This algebra is obtained from the universal enveloping algebra U(g) by a certain Hamiltonian reduction. We observe that W is the invariant algebra for an action of a reductive group G with Lie algebra g on a quantized symplectic affine variety and use this observation to study W. Our results include an alternative definition of W, a relation between the sets of prime ideals of W and of the corresponding universal enveloping algebra, the existence of a one-dimensional representation of W in the case of classical g and the separation of elements of W by finite dimensional representations.
Source: arXiv (Cornell University)
Author: Losev, Ivan
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951949693