arXiv:2308.13120v1 [math.QA] 25 Aug 2023 Page 1 arXiv:2308.13120v1 [math.QA] 25 Aug 2023
ON INFINITE-DIMENSIONAL HOPF ALGEBRAS NICOLÁS ANDRUSKIEWITSCH Dedicated to …

We classify finite-dimensional pointed Hopf algebras with abelian coradical, up to
isomorphism, and show that they are cocycle deformations of the associated graded Hopf …

Lifting via cocycle deformation Page 1 Journal of Pure and Applied Algebra 218 (2014) 684–703
Contents lists available at ScienceDirect Journal of Pure and Applied Algebra journal …

Let $ H_8 $ be the neither commutative nor cocommutative semisimple eight dimensional
Hopf algebra, which is also called Kac-Paljutkin algebra\cite {MR0208401}. All simple Yetter …

Abstract The 12-dimensional Fomin–Kirillov algebra FK 3 is defined as the quadratic
algebra with generators a, b and c which satisfy the relations a 2= b 2= c 2= 0 and a b+ b c+ …

Using the standard filtration associated with a generalized lifting method, we determine all
finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero …

We study the pointed or copointed liftings of Nichols algebras associated to affine racks and
constant cocycles for any finite group admitting a principal YD-realization of these racks. In …

Classifying all Hopf algebras of a given finite dimension over C is a challenging problem
which remains open even for many small dimensions, not least because few general …

After the classification of the finite-dimensional Nichols algebras of diagonal type 17, 18, the
determination of its defining relations 7, 6, and the verification of the generation in degree-s1 …

This is a survey on spherical Hopf algebras. We give criteria to decide when a Hopf algebra
is spherical and collect examples. We discuss tilting modules as a mean to obtain a fusion …