On the semisolvability of semisimple Hopf algebras of low dimension

By Sonia Natale. 2003

55 citations recorded by the source corpus.

We prove that every semisimple Hopf algebra of dimension less than 60 over an algebraically closed field k of characteristic zero is either upper or lower semisolvable up to a cocycle twist.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3c3201dc9c590709ae54a3fd6028d714dde37329

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

WEAKLY GROUP-THEORETICAL AND SOLVABLE FUSION CATEGORIES (2008, background): “ consequences of Theorem 1.6). 2. Semisimple Hopf algebras of small dimension were studied extensively in the literature, see [N2, Table 1] for the list of references. In particular, in the monograph [N2] it is shown that semisimple Hopf algebras of dimension <60 are either upper or lower semisol”
On finite-dimensional Hopf algebras (2014, background): “To my knowledge, all examples of semisimple Hopf algebras arise from group algebras by the preceding constructions; this was proved in [68, 70] in low dimensions and in [32] for dimensions pq, pqr, where p, q and r are primes.”