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Semisimple finite-dimensional Hopf algebras

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Abstract

The paper considers a classification of semisimple Hopf algebras having exactly one irreducible non-one-dimensional representation under a certain condition on the number of group elements.

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References

  1. V. A. Artamonov, “Semisimple Finite-Dimensional Hopf Algebras,” Matem. Sbornik 198(9), 3 (2007).

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  2. V. A. Artamonov and I. A. Chubarov, “Dual Algebras of Some Semisimple Finite Dimensional Hopf Algebras,” in: Modules and Comodules (Birkhäuser, Basel, 2008), pp. 65–85.

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  3. R. B. Mukhatov, “On Semisimple Finite-Dimensional Hopf Algebras,” Fund. i Prikl. Matem. 15(2), 133 (2009).

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  4. E. M. Zhmud’, “Symplectic Geometries and Projective Representations of Finite Abelian Groups,” Matem. Sbornik 87(129) (1), 3 (1972).

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  5. V. A. Artamonov and I. A. Chubarov, “Properties of Some Semisimple Hopf Algebras,” in: Algebras, Representations and Applications (AMS, Providence, 2009), pp. 23–36.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    R. B. Mukhatov

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  1. R. B. Mukhatov
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Additional information

Original Russian Text © R.B. Mukhatov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 60–63.

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Mukhatov, R.B. Semisimple finite-dimensional Hopf algebras. Moscow Univ. Math. Bull. 66, 44–46 (2011). https://doi.org/10.3103/S0027132211010098

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  • DOI: https://doi.org/10.3103/S0027132211010098

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