2018/12/17 by Eduardo Dubuc, Anders Kock, Dubuc, Eduardo +1
Mathematics · #13A50 #51K10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A50 #msc:51K10
paper · pdf · doi:10.48550/arxiv.1812.07021
arxiv created 2018/12/17 · arxiv updated 2018/12/19
We study the polynomial algebra (over a ring containing the rationals) in an n by m matrix of variables, and subject to the relation that says that the product of any two variables in the same column is zero. We show that the sub-algebra of polynomials, which are invariant under n! permutations of the columns, is a quotient of the polynomial algebra in m variables; the quotient map sends the ith variable to the sum of the entries in the ith row of the matrix. - An application in synthetic differential geometry is sketched