Abstract Let Z (W) be the center of the finite W -algebra W (g, e) associated with g=Lie (G) and a nilpotent element e for a connected reductive algebraic group G over an algebraically closed field x1D55C of prime characteristic p under the standard hypotheses (H1) - (H3) (see 8, section 6·3). In this paper, we first demonstrate that our previous results in 20 on the structure and geometric properties of Z (W) for p0 are still true under the present weakened restriction on p. Then we study the Zassenhaus variety Z of W (g, e), which is by definition the maximal spectrum Specm (Z (W) ) of Z (W). On basis of the structure properties of Z (W), we describe Z via a good transverse slice S and show that Z is birationally equivalent to S, thereby a rational affine scheme. In the special case when e=0, we reobtain one of the main results of 26 on the rationality of the Zassenhaus varieites for reductive Lie algebras in prime characteristic.
SHU et al. (Mon,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: