On the bosonization of the super Jordan plane

  • Nicolás Andruskiewitsch
  • Dirceu BagioEmail author
  • Saradia Della Flora
  • Daiana Flôres


Let H and K be the bosonizations of the Jordan and super Jordan plane by the group algebra of a cyclic group; the algebra K projects onto an algebra L that can be thought of as the quantum Borel of \(\mathfrak {sl}(2)\) at \(-\,1\). The finite-dimensional simple modules over H and K, are classified; they all have dimension 1, respectively \(\le 2\). The indecomposable L-modules of dimension \(\le 5\) are also listed. An interesting monoidal subcategory of \({\text {rep}}\,L\) is described.


Super Jordan plane Representation Bosonization Borel subalgebra 

Mathematics Subject Classification

16G30 16G60 16T05 



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Copyright information

© Instituto de Matemática e Estatística da Universidade de São Paulo 2019

Authors and Affiliations

  1. 1.FaMAF-Universidad Nacional de Córdoba, CIEM (CONICET)CórdobaArgentine Republic
  2. 2.Departamento de MatemáticaUniversidade Federal de Santa MariaSanta MariaBrazil

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