Cocycle Deformations and Brauer Groups

Abstract

Let (H, R) be a finite coquasitriangular Hopf algebra over a commutative ring k with unity. In this article, we show that the exact sequence

for the equivariant Brauer group obtained in the article Zhang (2004), is stable under cocycle twisting for any cocycle σ:H⊗ H→ k on H.

Key Words:

• Azumaya algebra
• Brauer group
• Yetter–Drinfeld module

2000 Mathematics Subject Classification:

• 16H05
• 16W30

ACKNOWLEDGMENTS

The first author would like to thank the School of Mathematics, Statistics, and Computer Science, Victoria University of Wellington for their hospitality during his visit in 2004. He is grateful to the URF of VUW for the financial support. He is also supported by NSF of China (No. 10471121).

The second author is supported by the Marsden Fund.

Notes

Communicated by R. Wisbauer.