Dual pairs of quantum moment maps and doubles of Hopf algebras

Gus Schrader, Alexander Shapiro*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a dual pair of topological Hopf algebras A,A, under mild conditions there exists a natural associative algebra homomorphism D(A)→H(A) between the corresponding Drinfeld double D(A) and Heisenberg double H(A). We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck–Springer resolution arises in this context.

Original languageEnglish (US)
Pages (from-to)74-89
Number of pages16
JournalJournal of Algebra
StatePublished - Dec 15 2017
Externally publishedYes


  • Drinfeld double
  • Grothendieck–Springer resolution
  • Heisenberg double
  • Hopf algebras
  • Quantum groups
  • Quantum moment maps
  • Reflection equation algerbas

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'Dual pairs of quantum moment maps and doubles of Hopf algebras'. Together they form a unique fingerprint.

Cite this