Bulletin of the Belgian Mathematical Society - Simon Stevin

On a family of Hopf algebras of dimension 72

Nicolás Andruskiewitsch and Cristian Vay

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Abstract

We investigate a family of Hopf algebras of dimension 72 whose coradical is isomorphic to the algebra of functions on $\mathbb S_3$. We determine the lattice of submodules of the so-called Verma modules and as a consequence we classify all simple modules. We show that these Hopf algebras are unimodular (as well as their duals) but not quasitriangular; also, they are cocycle deformations of each other.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 3 (2012), 415-443.

Dates
First available in Project Euclid: 14 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1347642374

Mathematical Reviews number (MathSciNet)
MR3027352

Zentralblatt MATH identifier
1282.16036

Subjects
Primary: 16W30

Keywords
Representations of Hopf algebras

Citation

Andruskiewitsch, Nicolás; Vay, Cristian. On a family of Hopf algebras of dimension 72. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 415--443. https://projecteuclid.org/euclid.bbms/1347642374


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