Félix, Yves
[UCL]
Halperin, S.
Thomas, JC.
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.
Bibliographic reference |
Félix, Yves ; Halperin, S. ; Thomas, JC.. Elliptic Hopf-algebras. In: Journal of the London mathematical society, Vol. 43, p. 545-555 (1991) |
Permanent URL |
http://hdl.handle.net/2078.1/50933 |