On the Drinfeld doubles of Laistrygonian algebras in positive characteristic

@misc{andruskiewitsch2026drinfeld,
  title = {{On the Drinfeld doubles of Laistrygonian algebras in positive characteristic}},
  author = {Nicolás Andruskiewitsch and Dirceu Bagio and Saradia Della Flora and Daiana Flores and Oscar Márquez and Héctor Martín Peña Pollastri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16665},
  eprint = {2610.16665},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16665},
}

TY  - UNPB
TI  - On the Drinfeld doubles of Laistrygonian algebras in positive characteristic
AU  - Nicolás Andruskiewitsch
AU  - Dirceu Bagio
AU  - Saradia Della Flora
AU  - Daiana Flores
AU  - Oscar Márquez
AU  - Héctor Martín Peña Pollastri
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16665
UR  - https://arxiv.org/abs/2610.16665
AB  - In this work, we study restricted Laistrygonian algebras over a field of positive characteristic p. We compute their Drinfeld double D_p(q,a) and give explicit presentations by generators and relations. We prove that D_p(q,a) is a pointed Hopf algebra. For 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 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× 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.
ER  -