On the representation ring of the polynomial algebra over a perfect field
Representation Theory
2009-07-09 v1 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.0810.5240,
title = {On the representation ring of the polynomial algebra over a perfect field},
author = {Erik Darpö and Martin Herschend},
journal= {arXiv preprint arXiv:0810.5240},
year = {2009}
}
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17 pages