Some graded Hopf-module pseudoalgebras.

In this paper, we define a G -graded Hopf module associative pseudoalgebra A for any grading group G and Hopf algebra H , and construct a smash product A # H of A with H , which is also a G -graded associative pseudoalgebra. Then we establish a Mortia context between A # H and A H , the fixed sub-pseudoalgebra under the action of H. In addition, we prove a similarity of the Schur-Weyl type duality between the group algebra k [ S e (n) ] of Sergeev group S e (n) and a super pseudoalgebra. [ABSTRACT FROM AUTHOR]