An affine PI Hopf algebra not finite over a normal commutative Hopf subalgebra

摘要

In formulating a generalized framework to study certain noncommutative algebras naturally arising in representation theory, K. A. Brown asked if every finitely generated Hopf algebra satisfying a polynomial identity was finite over a normal commutative Hopf subalgebra. In this note we show that Radford's biproduct, applied to the enveloping algebra of the Lie superalgebra pl( 1; 1), provides a noetherian prime counterexample. [References: 14]