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arXiv · 2610.16665

On the Drinfeld doubles of Laistrygonian algebras in positive characteristic

Nicolás Andruskiewitsch·Dirceu Bagio·Saradia Della Flora·Daiana Flores·Oscar Márquez·Héctor Martín Peña Pollastri
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Abstract

In this work, we study restricted Laistrygonian algebras over a field of positive characteristic $p$. We compute their Drinfeld double $\mathtt{D_p(q,a)}$ and give explicit presentations by generators and relations. We prove that $\mathtt{D_p(q,a)}$ is a pointed Hopf algebra. For $\mathtt{D_p(1,a)}$, we describe an abelian exact sequence of Hopf algebras and identify one of its quotients as a restricted enveloping Lie algebra. This exact sequence enables us to classify the finite-dimensional simple $\mathtt{D_p(1,a)}$-modules. We also introduce an infinite-dimensional Hopf algebra covering the restricted Drinfeld double and study its relation with the corresponding finite-dimensional case. Using this covering together with a Frobenius map, we construct a $3\times 3$ commutative diagram whose rows and columns are exact sequences of Hopf algebras. In particular, our approach provides a unified treatment of the Drinfeld doubles associated with restricted Laistrygonian algebras in arbitrary positive characteristic.

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Nicolás Andruskiewitsch, Dirceu Bagio, Saradia Della Flora, Daiana Flores, Oscar Márquez, Héctor Martín Peña Pollastri. 2026-10-12. On the Drinfeld doubles of Laistrygonian algebras in positive characteristic. https://arxiv.org/abs/2610.16665

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