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arXiv · 2505.15569

On braided Hopf structures on exterior algebras

Rinat Kashaev·Vladimir Mangazeev
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Abstract

We show that the exterior algebra of a vector space $V$ of dimension greater than one admits a one-parameter family of braided Hopf algebra structures, arising from its identification with a Nichols algebra. We explicitly compute the structure constants with respect to a natural set-theoretic basis. A one-parameter family of diagonal automorphisms exists, which we use to construct solutions to the (constant) Yang--Baxter equation. These solutions are conjectured to give rise to the two-variable Links--Gould polynomial invariants associated with the super-quantum group $U_q(\mathfrak{gl}(N|1))$, where $N = \dim(V)$. We support this conjecture through computations for small values of $N$.

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BibTeXRIS

Rinat Kashaev, Vladimir Mangazeev. 2025-05-21. On braided Hopf structures on exterior algebras. https://doi.org/10.1016/j.jpaa.2025.108135

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