Hochschild cohomology and quantum Drinfeld Hecke algebras

• Deepak Naidu ^[1] ; Sarah Witherspoon ^[2]
  1. [1] Northern Illinois University

     Northern Illinois University

     Township of DeKalb, Estados Unidos

     
  2. [2] Texas A&M University

     Texas A&M University

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 3, 2016, págs. 1537-1561
• Idioma: inglés
• DOI: 10.1007/s00029-016-0224-3
• Enlaces
  • Texto completo
• Resumen

  • Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups, and we exploit computations from Naidu et al. (Proc Am Math Soc 139:1553–1567, 2011) for diagonal actions. By combining our work with recent results of Levandovskyy and Shepler (Can J Math 66:874–901, 2014) we produce examples of quantum Drinfeld Hecke algebras. These algebras generalize the braided Cherednik algebras of Bazlov and Berenstein (Selecta Math 14(3–4):325–372, 2009).