On the bosonization of the super Jordan plane

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 $$\\mathfrak {sl}(2)$$sl(2) at $$-\\,1$$-1. The finite-dimensional simple modules over H and K, are classified; they all have dimension 1, respectively $$\\le 2$$≤2. The indecomposable L-modules of dimension $$\\le 5$$≤5 are also listed. An interesting monoidal subcategory of $${\\text {rep}}\\,L$$repL is described.