In this paper, twisted modules for modular affine vertex algebras and for their quotient vertex algebras with a restricted Lie algebra are studied. Let be an automorphism of and let be a positive integer relatively prime with the characteristic such that . It is proved that -graded irreducible -twisted -modules are in one-to-one correspondence with irreducible modules for the restricted enveloping algebra , where is the subalgebra of -fixed points in . It is also proved that when is abelian, the twisted Heisenberg Lie algebra is actually isomorphic to the untwisted Heisenberg Lie algebra , unlike in the case of characteristic zero. Furthermore, irreducible -twisted -modules are classified and a complete reducibility is obtained.
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穆强，哈尔滨师范大学数学科学学院教授，主要研究领域为李代数和顶点代数，在Trans. Amer. Math. Soc.、J. Algebra等SCI杂志发表论文10余篇。现主持国家自然科学基金面上项目2项、黑龙江省基金一项，主持完成数学天元青年基金、黑龙江省基金、省教育厅新世纪人才、省教育厅科研项目各一项，2017年黑龙江省科学技术三等奖第一完成人。
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