Finite-dimensional Hopf superalgebras and graded pentagon equation. (English) Zbl 07904740
Summary: Suppose that \(H\) is an arbitrary finite-dimensional Hopf superalgebra. Let \(\mathcal{H}(H)\) be the Heisenberg double of \(H\) and let \(\mathcal{R}\) be the canonical matrix of \(\mathcal{H}(H)\) that satisfies the graded pentagon equation \(\mathcal{R}_{12} \mathcal{R}_{13} \mathcal{R}_{23} = \mathcal{R}_{23} \mathcal{R}_{12}\). It is established that \(H\) is isomorphic to the Hopf superalgebra \(\mathcal{P}(\mathcal{H}(H), \mathcal{R})\) of left coefficients of \(\mathcal{R}\). This result can be regarded as a generalisation of Militaru’s result [10] from the non-super situation to the super situation.
Keywords:
finite-dimensional Hopf superalgebras; graded pentagon equation; Heisenberg double; monoidal categoriesReferences:
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