Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897263 | Journal of Pure and Applied Algebra | 2019 | 20 Pages |
Abstract
We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form gâFF[t1,â¦,tâ]/I, where g is a finite-dimensional Lie algebra over a field F of characteristic zero, and I is a finite-codimensional ideal of F[t1,â¦,tâ] generated by monomials. In particular, when g is semisimple and F is algebraically closed, we construct a set of algebraically independent generators for the algebra of invariant polynomials. In addition, we describe a transversal slice to the space of regular orbits in gâFF[t1,â¦,tâ]/I. As an application of our main result, we show that the center of the universal enveloping algebra of gâFF[t1,â¦,tâ]/I acts trivially on all irreducible finite-dimensional representations provided I has codimension at least two.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Tiago Macedo, Alistair Savage,