Revista de la
Unión Matemática Argentina
The Green ring of a family of copointed Hopf algebras
Cristian Vay

Volume 68, no. 1 (2025), pp. 23–48    

Published online (final version): December 18, 2024

https://doi.org/10.33044/revuma.3622

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Abstract

The copointed liftings of the Fomin–Kirillov algebra $\mathcal{FK}_3$ over the algebra of functions on the symmetric group $\mathbb{S}_3$ were classified by Andruskiewitsch and the author. We demonstrate here that those associated to a generic parameter are Morita equivalent to the regular blocks of well-known Hopf algebras: the Drinfeld doubles of the Taft algebras and the small quantum groups $u_{q}(\mathfrak{sl}_2)$. The indecomposable modules over these were classified independently by Chen, Chari–Premet and Suter. Consequently, we obtain the indecomposable modules over the generic liftings of $\mathcal{FK}_3$. We decompose the tensor products between them into the direct sum of indecomposable modules. We then deduce a presentation by generators and relations of the Green ring.

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