Searcharxiv⌕ Search
Home/Archive/arXiv

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
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

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

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deformation quantization of symplectic vector fields

In this paper, we study deformation quantization of symplectic vector fields à la Fedosov. We provide an explicit construction to quantize each symplectic vector field as a derivation of the deformed star algebra. This recovers a result of Müller-Bahns and Neumaier with an explicit formula of higher total degree terms. Moreover, we show that this quantization yields a non-abelian $2$-cocycle on the Lie algebra of symplectic vector fields with values in the deformed star algebra. For a Fedosov deformation quantization with vanishing first characteristic class, this non-abelian $2$-cocycle can provide a formal deformation of the crossed-product algebra generated by the action of symplectic vector fields. In this sense, we can quantize any Lie algebra action by symplectic vector fields.

math.QA↗
arXiv2026

Evaluation-type deformed modules over the quantum affine vertex algebras of type $A$

Let $\mathcal{V}^c(\mathfrak{gl}_N)$ be Etingof-Kazhdan's quantum affine vertex algebra associated with the trigonometric $R$-matrix. We establish a connection between suitably generalized deformed $ϕ$-coordinated $\mathcal{V}^c(\mathfrak{gl}_N)$-modules and the representations of quantized enveloping algebra $U_h(\mathfrak{gl}_N)$ and reflection equation algebra $\mathcal{O}_h(Mat_N)$. As an application, we demonstrate how the elements of the center of $\mathcal{V}^c(\mathfrak{gl}_N)$ at the critical level $c=-N$ give rise to the $q$-analogues of quantum immanants for $U_h(\mathfrak{gl}_N)$, which were recently found by Jing, Liu and Molev. Finally, we derive the analogues of these results for the quantum affine vertex algebra associated with the normalized Yang $R$-matrix.

math.QA↗
arXiv2026

Local Ocneanu rigidity for separable algebra objects

We establish local Ocneanu rigidity for separable algebra objects in Hom-finite monoidal categories C over an algebraically closed field k. A separability morphism contracts the first two Hochschild cohomology groups without requiring an abelian ambient category. Separable algebra structures and homomorphisms from separable sources have open algebraic-group orbits, and affine Bezout estimates give effective finiteness results. For Frobenius subalgebras, exchange relations replace the source and embedding data by a single self-dual idempotent. We prove that their separable inner-conjugacy classes are open in the exchange locus, yielding a bound of 2^(dim_k(End_C(X))) for any ambient Frobenius algebra X; connectedness gives the same bound on the actual number of subalgebras. As an application, we obtain an effective form of the Etingof-Walton finiteness theorem: every finite-dimensional semisimple Hopf algebra H over C has fewer than 2^(dim_C(H)) left coideal subalgebras. In the unitary setting, we bound E-compatible intermediates of C*-algebra and von Neumann algebra inclusions up to unitary conjugacy, under finite-index and finite-center hypotheses. For irreducible finite-index subfactors N < M, we improve the 9^[M:N] bound of Bakshi-Das-Liu-Ren to fewer than 2^[M:N] intermediate subfactors.

math.QA↗