Classification of Semisimple Hopf Algebras of Dimension 16
By Yevgenia Kashina. 2000
69 citations recorded by the source corpus.
Abstract In this paper we completely classify nontrivial semisimple Hopf algebras of dimension 16. We also compute all the possible structures of the Grothendieck ring of semisimple non-commutative Hopf algebras of dimension 16. Moreover, we prove that non-commutative semisimple Hopf algebras of dimension pn, p-prime, cannot have a cyclic group of grouplikes.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/188d18a7e2fbd98da63e8f03f9387844ccac29ca
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In Algebra and Number Theory
- D. Nikshych
- V. Ostrik
- Shlomo Gelaki
- V. Drinfeld
- D. Venku Naidu
- C. Calinescu
- V. Linchenko
- S. Dascalescu
In Geometry and Topology
- D. Nikshych
- V. Ostrik
- Shlomo Gelaki
- V. Drinfeld
- D. Venku Naidu
- C. Calinescu
- V. Linchenko
- S. Dascalescu
Citations in the corpus
- Quantum lines over non-cocommutative cosemisimple Hopf algebras (2004, background): “Pointed Hopf algebras of dimension 16 are classified in [10], and semisimple Hopf algebras of dimension 16 are classified in [ 12 ].”
- A Frobenius–Schur Theorem for Hopf Algebras (2000, methodology): “The coalgebra structure of H is given explicitly in [ K2 ] as follows:”
- GROUP-THEORETICAL PROPERTIES OF NILPOTENT MODULAR CATEGORIES (2007, methodology): “Remark 6.9. Semisimple Hopf algebras of dimension p n were studied by several authors, see e.g., [EG2], [ Kash ], [Ma1], [Ma2], [MW], [Z].”