arXiv subjects

M. Beattie

Publications and source records attributed to M. Beattie.

4 recordsLinked to original sources

arXiv2012

Stable equivalence of Morita type and Frobenius extensions

A.S. Dugas and R. Martínez-Villa proved in \cite[Corollary 5.1]{dm} that if there exists a stable equivalence of Morita type between the $k$-algebras $Λ$ and $Γ$, then it is possible to replace $Λ$ by a Morita equivalent $k$-algebra $Δ$ such that $Γ$ is a subring of $Δ$ and the induction and restriction functors induce inverse stable equivalences. In this note we give an affirmative answer to a question of Alex Dugas about the existence of a $Γ$-coring structure on $Δ$. We do this by showing that $Δ$ is a Frobenius extension of $Γ$.

math.RA↗

arXiv2007

Duals of pointed Hopf algebras

This paper studies the duals of some finite dimensional pointed Hopf algebras, with abelian group of grouplikes, over an algebraically closed field of characteristic 0, which are either Radford biproducts or else nontrivial liftings of a biproduct.

math.QA↗

arXiv2006

Irreducible representations of liftings of quantum planes

In this note, the irreducible representations of a lifting of a quantum plane are determined. Both authors thank Hans-Jürgen Schneider for pointing out a mistake in the published version of the paper, that is corrected here.

math.RT↗

arXiv2003

Hopf algebras of dimension 14

Let H be a finite dimensional non-semisimple Hopf algebra over an algebraically closed field k of characteristic 0. If H has no nontrivial skew-primitive elements, we find some bounds for the dimension of H_1, the second term in the coradical filtration of H. Using these results, we are able to show that every Hopf algebra of dimension 14 is semisimple and thus isomorphic to a group algebra or the dual of a group algebra. Also a Hopf algebra of dimension pq where p and q are odd primes with p<q and q less than or equal to 1 + 3p, and also less than or equal to 13, is semisimple and thus a group algebra or the dual of a group algebra. We also have some partial results in the classification problem for dimension 16.

math.QA↗