Column symmetric polynomials

DUBUC EDUARDO J.; KOCK ANDERS

CAHIERS DE TOPOLOGIE ET GEOMETRIE DIFFERENTIELLE CATEGORIQUES

Amiens

Lugar: Amiens; Año: 2019 vol. 60 p. 241 - 254

0008-0004

We study the polynomial algebra (over a ring containing the rationals)in an m by n matrix of variables, and subject to the relation that saysthat the product of any two variables in the same column is zero. Weshow that the sub-algebra of polynomials, which are invariant under the n! permutations of the columns, is a quotient of the polynomial algebra in m variables; the quotient map sends the i´th variable to the sum of the entries in the i´th row of the matrix. An application in synthetic differential geometry is sketched.Keywords. Symmetric polynomials, synthetic differential geometry.Mathematics Subject Classification (2010). 13A50, 51K10