Elliptic Hopf-algebras

An elliptic Hopf algebra is a connected graded cocommutative Hopf algebra that is finitely generated and nilpotent. If (A,m,k) is a local noetherian ring then Ext(A)(k; k) is elliptic if and only A is a complete intersection. Similarly, special conditions are imposed on a simply connected topological space X if H*(OMEGA-X; k) is elliptic. Elliptic Hopf algebras G have finite depth and we show that they are characterized among Hopf algebras of finite depth by any of the following three properties: (i) SIGMA-i less-than-or-equal-to n dim G(i) grows at most polynomially in n; (ii) G is left noetherian; (iii) G is nilpotent.