PBW-deformations of smash products involving Hopf algebra of Kac-Paljutkin type

2024/08/29 by Gao, Yujie, Yang, Shilin
#16S37 #16S40 #16S80 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.16557

Abstract

Let H_2n² be the Kac-Paljutkin type Hopf algebra of dimension 2n², A its graded Koszul Artin-Schelter regular H_2n²-module algebra of dimension 2, A^! the Koszul dual of A, and A^op_c the braided-opposite algebra of A. This paper describes (0, 1)-degree PBW-deformations of the smash product A \sharp H_2n² and those of A^! \sharp H_2n² under the condition that the Koszul dual A^! of A is also an H_2n²-module algebra. Also, 0-degree PBW-deformations of (A ⊗^c A^op_c) \sharp H_2n² are explored, where A ⊗^c A^op_c is the associated braided tensor product algebra.

Related

• PBW deformations of braided products
• Deformation Theory and Hopf Actions on Koszul Algebras
• PBW deformations of Koszul algebras over a nonsemisimple ring
• Generalized Kac-Paljutkin algebras
• L-R-smash product for (quasi) Hopf algebras