Mathematics

Given a n-dimensional vector space V , we define a cubic algebra F = F(V) generated by V, which is regular of global dimension n(n+1)/2(in the sense of Artin-Schelter) and which is a model for the polynomial representations of GL(V) which acts by automorphisms on F(i.e. each Young diagram representation appears with multiplicity one).This algebra is not 3-Koszul but we describe its Yoneda algebra E(F) in terms of its GL(V)-representations content and we give some properties of its canonical A_\infty-structure and make explicit its Frobenius algebrastructure corresponding to the Poincare duality property of F.