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A minimal set of generators for the ring of multisymmetric functions
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-2505-6417
2007 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, Vol. 57, no 6, 1741-1769 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this article is to give, for any (commutative) ring A, an explicit minimal set of generators for the ring of multisymmetric functions TSAd[x(1),...,x(r)]) = (A[x(1),...,x(r)](circle times)A(d))8(d) A as an A-algebra. In characteristic zero, i.e. when A is a Q-algebra, a minimal set of generators has been known since the 19(th) century. A rather si-nall generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound oil the generators, improving the degree bound previously obtained by Fleischmann. As Gamma(d)(A) (A[x(1),...,x(r)]) = TSAd (A[x(1),...,x(r)]) we also obtain generators for di A vided powers algebras: If B is a finitely generated A-algebra with a given surjection A[x(1), x(2),...,x(r)] --> B then using the corresponding surjection Gamma(d)(A) (A[x(1),...,x(r)]) --> Gamma(d)(A) (B) we get generators for Gamma(d)(A) (B).

Place, publisher, year, edition, pages
2007. Vol. 57, no 6, 1741-1769 p.
Keyword [en]
symmetric functions, generators, divided powers, vector invariants
National Category
URN: urn:nbn:se:kth:diva-37132ISI: 000252868000001ScopusID: 2-s2.0-38349187610OAI: diva2:432189
Available from: 2011-08-01 Created: 2011-08-01 Last updated: 2011-08-01Bibliographically approved

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Rydh, David
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