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On the representation ring of the polynomial algebra over a perfect field
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic.
2010 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 265, no 3, 601-615 p.Article in journal (Refereed) Published
Abstract [en]

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) over tilde is provided.

Place, publisher, year, edition, pages
2010. Vol. 265, no 3, 601-615 p.
Keyword [en]
Representation ring, Polynomial algebra, Quiver representation, Tensor product, Clebsch-Gordan problem
National Category
URN: urn:nbn:se:uu:diva-136561DOI: 10.1007/s00209-009-0532-9ISI: 000277603500007OAI: oai:DiVA.org:uu-136561DiVA: diva2:377301
Available from: 2010-12-14 Created: 2010-12-13 Last updated: 2016-04-29Bibliographically approved

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Herschend, Martin
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Algebra, Geometry and Logic
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