Note on Primitive Ideals of Enveloping Algebras in Prime Characteristic

作者：Yao, Yufeng^*

来源：Algebra Colloquium, 2011, 18(4): 701-708.

DOI：10.1142/S1005386711000551

• primitive ideal
• annihilator
• center
• Zassenhaus variety
• baby Verma module

Let g be a restricted Lie algebra over an algebraically closed field F of characteristic p > 0, Z (g) the center of the universal enveloping algebra U(g) of g. In this note, we study primitive ideals of U(g). The following results are included: (1) The ideal of U(g) generated by the central character ideal associated with any irreducible g-module has finite co-dimension in U(g). Furthermore, the co-dimension is no less than d(g)(2), where d(g) is the maximal dimension of irreducible g-modules. (2) Each annihilator ideal of irreducible g-modules of maximal dimension is generated by the corresponding central character ideal in Z (g). (3) Each G-stable ideal in U(g) for g = Lie(G) contains nonzero fixed points under the action of G, where G is a connected reductive algebraic group. Additionally, the arguments on ideals help us to give an alternative description of the Azumaya locus in the Zassenhaus variety without using the normality of the Zassenhaus variety.

• 出版日期2011-12
• 单位上海海事大学