Duffy, Colleen M.. Graded traces and irreducible representations of Aut(A(Gamma)) acting on graded A(Gamma) and A(Gamma)!. Retrieved from https://doi.org/doi:10.7282/T3K074MR
DescriptionIn this work we will study the structure of algebras A(Gamma) associated to directed, layered graphs. The algebras for which we find a decomposition are the algebras related to
pseudo-roots of noncommutative polynomials and algebras associated to the Hasse graphs of polytopes, to the lattice of subspaces of a
finite-dimensional vector space over a finite field, and to the complete layered graph. We will first find the filtration-preserving automorphism group of these algebras and develop methods of calculating the graded trace of an automorphism acting on the algebra. We will then find the multiplicities of the irreducible representations of Aut(A(Gamma)) acting on the
homogeneous components of A(Gamma) and A(Gamma)^!. The methods developed lead us to consider subalgebras of graded A(Gamma).