A minimal set of generators for the ring of multisymmetric functions
2007 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, Vol. 57, no 6, 1741-1769 p.Article in journal (Refereed) Published
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.
symmetric functions, generators, divided powers, vector invariants
IdentifiersURN: urn:nbn:se:kth:diva-37132ISI: 000252868000001ScopusID: 2-s2.0-38349187610OAI: oai:DiVA.org:kth-37132DiVA: diva2:432189