Induced modules of strongly group-graded algebras
Various results on the induced representations of group rings are extended to modules over strongly group-graded rings. In particular, a proof of the graded version of Mackey's theorem is given.
Invariants of Lie color algebras acting on graded algebras
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials
In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.