The Dixmier-Moeglin equivalence for cocommutative Hopf algebras of finite Gelfand-Kirillov dimension Institutional Repository Document uri icon

abstract

  • Let $k$ be an algebraically closed field of characteristic zero and let $H$ be a noetherian cocommutative Hopf algebra over $k$. We show that if $H$ has polynomially bounded growth then $H$ satisfies the Dixmier-Moeglin equivalence. That is, for every prime ideal $P$ in ${
    m Spec}(H)$ we have the equivalences $$P~{
    m primitive}iff P~{
    m rational}iff P ~{
    m locally~closed~in}~{
    m Spec}(H).$$ We observe that examples due to Lorenz show that this does not hold without the hypothesis that $H$ have polynomially bounded growth. We conjecture, more generally, that the Dixmier-Moeglin equivalence holds for all finitely generated complex noetherian Hopf algebras of polynomially bounded growth.

author list (cited authors)

  • Bell, J. P., & Leung, W. H.

complete list of authors

  • Bell, Jason P||Leung, Wing Hong

publication date

  • March 2014