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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.

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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