A Note on Regular Crossed Products and Galois Representations

Abstract

A crossed product representing an associative finite dimensional central simple algebra over a field is called regular if all values of the corresponding cocycle are roots of unity. Under a certain assumption such a crossed product is shown to allow the construction of Galois representations. The case of number fields is investigated more closely and several examples are discussed.

Key Words:

• Central simple algebras
• Galois cohomology
• Galois theory of number fields

Mathematics Subject Classification (2000):

• 12A80
• 11R32
• 11R34

ACKNOWLEDGMENT

I am grateful to the referee for some useful criticism.

Notes

Communicated by C. Cibils.