Abstract
Let G be the symmetric group \({{\mathbb S}_m}\). It is an important open problem whether the dimension of the Nichols algebra \({\mathfrak{B} (\mathcal{O},\rho)}\) is finite when \(\mathcal{O}\) is the class of the transpositions and ρ is the sign representation, with m ≥ 6. In the present paper, we discard most of the other conjugacy classes showing that very few pairs \({(\mathcal{O},\rho)}\) might give rise to finite-dimensional Nichols algebras.
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This work was partially supported by CONICET, ANPCyT and Secyt (UNC).
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Andruskiewitsch, N., Fantino, F. & Zhang, S. On pointed Hopf algebras associated with the symmetric groups. manuscripta math. 128, 359–371 (2009). https://doi.org/10.1007/s00229-008-0237-0
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DOI: https://doi.org/10.1007/s00229-008-0237-0