On rigidity of Nichols algebras

• Iván Angiono ^[1] ; Mikhail Kochetov ^[2] ; Mitja Mastnak ^[3]
  1. [1] Universidad Nacional de Córdoba

     Universidad Nacional de Córdoba

     Argentina

     
  2. [2] Memorial University of Newfoundland

     Memorial University of Newfoundland

     Canadá

     
  3. [3] Saint Mary's University

     Saint Mary's University

     Canadá

     

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• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 12 (December 2015), 2015, págs. 5539-5559
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.05.032
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• Resumen

  • We study deformations of graded braided bialgebras using cohomological methods. In particular, we show that many examples of Nichols algebras, including the finite-dimensional ones arising in the Andruskiewitsch–Schneider program of classification of pointed Hopf algebras, are rigid. This result can be regarded as nonexistence of “braided Lie algebras” with nontrivial bracket.