2004/08/24 by S. Caenepeel, Caenepeel, S., F. Van Oystaeyen +3
Mathematics · #16A16 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16A16
paper · pdf · doi:10.48550/arxiv.math/0408334
13 pages
arxiv created 2004/08/24 · arxiv updated 2009/12/01
We consider the Brauer group \rm BM'(k,G) of a group G (finite or infinite) over a commutative ring k with identity. A split exact sequence 1\longrightarrow \rm Br'(k)\longrightarrow \rm BM'(k,G)\longrightarrow \rm Gal(k,G) \longrightarrow 1 is obtained. This generalizes the Fröhlich-Wall exact sequence from the case of a field to the case of a commutative ring, and generalizes the Picco-Platzeck exact sequence from the finite case of G to the infinite case of G. Here \rm Br'(k) is the Brauer-Taylor group of Azumaya algebras (not necessarily with unit). The method developed in this paper might provide a key to computing the equivariant Brauer group of an infinite quantum group.