On the representation ring of the polynomial algebra over a perfect field
arXiv:0810.5240 · doi:10.1007/s00209-009-0532-9
Abstract
We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is made explicit in the special cases when k is real closed respectively algebraically closed. Furthermore, we discuss the generalisation of this problem to representations of quivers. In particular the representation ring of quivers of extended Dynkin type A is provided.
17 pages