arXiv subjects

Deividi Pansera

Publications and source records attributed to Deividi Pansera.

2 recordsLinked to original sources

arXiv2017

A class of semisimple Hopf algebras acting on quantum polynomial algebras

We construct a class of non-commutative, non-cocommutative, semisimple Hopf algebras of dimension $2n^2$ and present conditions to define an inner faithful action of these Hopf algebras on quantum polynomial algebras, providing, in this way, more examples of semisimple Hopf actions which do not factor through group actions. Also, under certain condition, we classify the inner faithful Hopf actions of the Kac-Paljutkin Hopf algebra of dimension $8$, $H_8$, on the quantum plane.

math.RA↗

arXiv2016

A note on a paper by Cuadra, Etingof and Walton

We analyse the proof of the main result of a paper by Cuadra, Etingof and Walton, which says that any action of a semisimple Hopf algebra $H$ on the $n$th Weyl algebra $A=A_n(K)$ over a field $K$ of characteristic $0$ factors through a group algebra. We verify that their methods can be used to show that any action of a semisimple Hopf algebra $H$ on an iterated Ore extension of derivation type $A=K[x_1;d_1][x_2;d_2][\cdots][x_n;d_n]$ in characteristic zero factors through a group algebra.

math.RA↗