On the representation ring of the polynomial algebra over a perfect field

Details On the representation ring of the polynomial algebra over a perfect field On the representation ring of the polynomial algebra over a perfect field

2008-10-29

arxiv.org/abs/0810.5240v1

Mathematics

Representation Theory

17 pages

Scientific paper

10.1007/s00209-009-0532-9

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.

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