PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type (2408.16557v3)

Abstract: This paper concerns the Kac-Paljutkin type Hopf algebra $H_{2n^2}$ and its grading Artin-Schelter regular $H_{2n^2}$-module algebra $A$ of dimension $2$. It is described that all PBW-deformations of the smash product $A \sharp H_{2n^2},$ and all PBW-deformations of $A^! \sharp\, H_{2n^2}$ under the conditions that the Koszul dual of $A$ is an $H_{2n^2}$-module algebra. Also, the nontrivial PBW-deformations of $(A \otimes^c A^{\mathrm{op}}_c) \sharp\, H_{2n^2}$ are explored, where $A \otimes^c A^{\mathrm{op}}_c$ is the associated braided tensor product algebra.