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Categories of Modules over Semisimple Finite-Dimensional HOPF Algebras

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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.

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References

  1. 1.

    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).

    MathSciNet  MATH  Google Scholar 

  2. 2.

    V. A. Artamonov, “Semisimple Hopf algebra,” Chebyshevskii Sb., 15, No. 1, 1–12 (2014).

    MathSciNet  Google Scholar 

  3. 3.

    V. A. Artamonov, “Semisimple Hopf algebras with restrictions on irreducible non-one-dimensional modules,” St. Petersburg Math. J., 26, No. 2, 207–223 (2015).

    MathSciNet  Article  Google Scholar 

  4. 4.

    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.

  5. 5.

    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.

    Google Scholar 

  6. 6.

    S. Natale and J. Y. Plavnik, “On fusion categories with few irreducible degrees,” Algebra and Number Theory, 6, No. 6, 1171–1197 (2012).

  7. 7.

    S. Yu. Spiridonova, “On some semisimple Hopf algebras of dimension n(n + 1),” Mat. Zametki, 91, No. 2, 253–269 (2012).

    MathSciNet  Article  Google Scholar 

  8. 8.

    S. Yu. Spiridonova, “Generalized commutativity of some Hopf algebras and their connections with finite fields,” Algebra Analysis, 25, No. 5, 202–220 (2013).

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Correspondence to V. A. Artamonov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 5–18, 2016.

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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

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