Pointed hopf algebras of dimension 32

By M. Graña. 2000

50 citations recorded by the source corpus.

We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with chark k ≠ 2. It turns out that there are infinite families of isomorphism classes of pointed Hopf algebras of dimension 32. In [AS1], [BDG] and [Ge] are given families of counterexamples for the tenth Kaplansky conjecture. Up to now, 32 is the lowest dimension where Kaplansky conjecture fails.

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

View Paper: https://www.semanticscholar.org/paper/d5ffaf7950451ce458b899d996f9dfbc2331ed94

Citations in the corpus

• Finite quantum groups over abelian groups of prime exponent (2000, unknown): “Other classification results of pointed Hopf algebras are known for some fixed dimension d: d = p(2) is easy and follows from [29,30];d = p(3) was done in [4], and by different methods in [10,36]; d = p(4) in [6] (and does not seem to be possible via the other methods); = 16 in [11], d = 32 in [17];”