The Green ring of a family of copointed Hopf algebras

• Cristian Vay ^[1]
  1. [1] Facultad de Matem´atica, Astronom´ıa, F´ısica y Computaci´on, Universidad Nacional de C´ordobaArgentina
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 1, 2025, págs. 23-48
• Idioma: inglés
• DOI: 10.33044/revuma.3622
• Enlaces
  • Texto completo
• Resumen

  • The copointed liftings of the Fomin–Kirillov algebra FK3 over the algebra of functions on the symmetric group S3 were classified by Andruskiewitsch and the author. We demonstrate here that those associated to a generic parameter are Morita equivalent to the regular blocks of well-known Hopf algebras: the Drinfeld doubles of the Taft algebras and the small quantum groups uq(sl2). The indecomposable modules over these were classified independently by Chen, Chari–Premet and Suter. Consequently, we obtain the indocomposable modules over the generic liftings of FK3. We decompose the tensor products between them into the direct sum of indecomposable modules. We then deduce a presentation by generators and relations of the Green ring.

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