The strong Brauer group of a cocommutative coalgebraThe strong Brauer group of a cocommutative coalgebra
Faculty of Sciences. Mathematics and Computer Science
Journal of pure and applied algebra. - Amsterdam
171(2002):1, p. 1-15
University of Antwerp
Using strong equivalences for coalgebras we define the strong Brauer group of a cocommutative coalgebra C, which is a subgroup of the Brauer group of C. In general there is not a good relation between the Brauer group of a coalgebra and the Brauer group of the dual algebra C-*, the former is not even a torsion group. We find that this subgroups embeds in the Brauer group of C-*. A key tool in this result is the use of techniques from torsion theory. Some cases where both subgroups coincide are shown, for example, C being coreflexive. (C) 2002 Elsevier Science B.V. All rights reserved.