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arXiv · 1903.06219

On the Bosonization of the Super Jordan Plane

Nicolás Andruskiewitsch·Dirceu Bagio·Saradia Della Flora·Daiana Flôres
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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 $\leq 5$ are also listed. An interesting monoidal subcategory of $\operatorname{rep} L$ is described.

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Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora, Daiana Flôres. 2019-03-14. On the Bosonization of the Super Jordan Plane. https://doi.org/10.1007/s40863-019-00125-8

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