Abstract (EN):
Any finite set of linear operators on an algebra A yields an operator algebra B and a module structure on A, whose endomorphism ring is isomorphic to a subring A(B) of certain invariant elements of A. We show that if A is a critically compressible left B-module, then the dimension of its self-injective hull (A) over cap over the ring of fractions of A(B) is bounded by the uniform dimension of A and the number of linear operators generating B. This extends a known result on irreducible Hopf actions and applies in particular to weak Hopf action. Furthermore we prove necessary and sufficient conditions for an algebra A to be critically compressible in the case of group actions, group gradings and Lie actions.
Language:
English
Type (Professor's evaluation):
Scientific