Hopf Algebras and a Counterexample to a Conjecture of Anick Original Research Article

Let A be a graded algebra of finite type over a field image. Anick has conjectured that if A has finite global dimension then A is linearly isomorphic to a graded polynomial algebra. When the ground field has odd characteristic we give a counterexample which is a cocommutative graded Hopf algebra. We also show that in this context the conjecture is true in characteristic zero or two and is almost true in odd characteristic. We propose a companion conjecture for Ext A(image, image) and prove it when A = UL, some graded Lie algebra L.