Abstract
There is given a construction of a series of semisimple finite-dimensional Hopf algebras having a single irreducible representation of dimension greater than 1. This dimension is equal to the number of one-dimensional representations.
Similar content being viewed by others
References
V. A. Artamonov, “On semisimple Hopf algebras with few representations of dimension greater than one,” Rev. Unión Mat. Argentina, 51, No. 2, 91–105 (2010).
V. A. Artamonov, “Semisimple Hopf algebra,” Chebyshevskii Sb., 15, No. 1, 1–12 (2014).
V. A. Artamonov, “Semisimple Hopf algebras with restrictions on irreducible non-one-dimensional modules,” St. Petersburg Math. J., 26, No. 2, 207–223 (2015).
V. A. Artamonov and I. A. Chubarov, “Dual algebras of some semisimple finite dimensional Hopf algebras,” in: Modules and Comodules, Trends in Math., Birkhäuser, Basel (2008), pp. 65–85.
V. A. Artamonov and I. A. Chubarov, “Properties of some semisimple Hopf algebras,” in: V. Futorny, V. Kac, I. Kashuba, and E. Zelmanov, eds., Algebras, Representations and Applications, A Conf. in Honour of Ivan Shestakov’s 60th Birthday, August 26 — September 1, 2007, Maresias, Brazil, Contemp. Math., Vol. 483, Amer. Math. Soc., Providence (2009), pp. 23–36.
S. Natale and J. Y. Plavnik, “On fusion categories with few irreducible degrees,” Algebra and Number Theory, 6, No. 6, 1171–1197 (2012).
S. Yu. Spiridonova, “On some semisimple Hopf algebras of dimension n(n + 1),” Mat. Zametki, 91, No. 2, 253–269 (2012).
S. Yu. Spiridonova, “Generalized commutativity of some Hopf algebras and their connections with finite fields,” Algebra Analysis, 25, No. 5, 202–220 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 5–18, 2016.
Rights and permissions
About this article
Cite this article
Artamonov, V.A. Categories of Modules over Semisimple Finite-Dimensional HOPF Algebras. J Math Sci 248, 513–523 (2020). https://doi.org/10.1007/s10958-020-04893-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-020-04893-z