Invariants of Domains under the Actions of Restricted Lie Algebras Original Research Article

The goal of this paper is to examine the relationship between a domain R and its subring of invariants RL, under the action of a finite-dimensional restricted Lie algebra L. We first show that there exists a nondegenerate (RL, RL)-bimodule "trace-like" map g: R → RL and therefore I ∩ RL ≠ 0, for every ideal I ≠ 0 of R. Next, we show that there exists a right RL-module embedding φ of R into a finite direct sum of copies of RL. Using the maps g and φ, we obtain the following, which is a combination of several of the main results of this paper.