Twisted modules for affine vertex algebras over fields of prime characteristic

In this paper, twisted modules for modular affine vertex algebras V-(g) over cap(l, 0) and for their quotient vertex algebras V-(g) over cap(chi)(l, 0) with g a restricted Lie algebra are studied. Let sigma be an automorphism of g and let T be a positive integer relatively prime with the characteristic p such that sigma(T) = 1. It is proved that 1/TN-graded irreducible sigma-twisted V-(g) over cap(0)(l, 0)-modules are in one-to-one correspondence with irreducible modules for the restricted enveloping algebra u(g(0)), where g(0) is the subalgebra of sigma-fixed points in g. It is also proved that when g = h is abelian, the twisted Heisenberg Lie algebra (h) over cap[sigma] is actually isomorphic to the untwisted Heisenberg Lie algebra (h) over cap, unlike in the case of characteristic zero. Furthermore, for any nonzero level l, irreducible sigma-twisted L-(h) over cap(l, 0)-modules are explicitly classified and the complete reducibility of every sigma-twisted L-(h) over cap(l, 0)-module is obtained. (C) 2019 Elsevier Inc. All rights reserved.