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On the bosonization of the super Jordan plane

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Abstract

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.

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Authors and Affiliations

  1. FaMAF-Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende s/n, Ciudad Universitaria, 5000, Córdoba, Argentine Republic

    Nicolás Andruskiewitsch

  2. Departamento de Matemática, Universidade Federal de Santa Maria, Santa Maria, RS, 97105-900, Brazil

    Dirceu Bagio, Saradia Della Flora & Daiana Flôres

Authors
  1. Nicolás Andruskiewitsch
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  2. Dirceu Bagio
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  3. Saradia Della Flora
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  4. Daiana Flôres
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Correspondence to Dirceu Bagio.

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Dedicated to Professor Ivan Shestakov on the occasion of his 70th birthday.

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Nicolás Andruskiewitsch was partially supported by CONICET, MATHAMSUD, Secyt (UNC). Dirceu Bagio and Daiana Flôres were supported by FAPERGS 2193-25.51/13-3, MATHAMSUD.

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Andruskiewitsch, N., Bagio, D., Della Flora, S. et al. On the bosonization of the super Jordan plane. São Paulo J. Math. Sci. 13, 1–26 (2019). https://doi.org/10.1007/s40863-019-00125-8

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  • DOI: https://doi.org/10.1007/s40863-019-00125-8

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