Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T16:58:45.414Z Has data issue: false hasContentIssue false
  • English
  • Français

Division Graded Algebras in the Brauer-Wall Group

Published online by Cambridge University Press:  20 November 2018

Francis Coghlan  and
Peter Hoffman
Francis Coghlan
Affiliation:
Mathematics Department, Manchester University, Manchester, England, M13 9PL
Peter Hoffman
Affiliation:
Pure Mathematics Department, Waterloo, Ontario, N2L 3G1
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that every element in the Brauer-Wall group of a field with characteristic different from 2 is represented uniquely by a division graded algebra, (i.e. homogeneous elements are invertible) but, of course, not necessarily by a graded (division algebra). This is a fairly direct consequence of Wall's structure theory for central simple Z/2-graded algebras.

Keywords

13A20graded algebradivision algebraBrauer-Wall group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 21 - 24
Copyright
Copyright © Canadian Mathematical Society 1995

References

[H] Hoffman, P. N., On the Schur index of graded representations; preprint.Google Scholar
[L] Lam, T. Y., The algebraic theory of quadratic forms, Benjamin, W. A., Reading, Mass. 1973.Google Scholar
[T] Turull, A., The Schur index of projective characters of symmetric and alternating groups, Ann. Math. 135(1992), 91–124.Google Scholar
[W] Wall, C. T. C., Graded Brauer Groups, J. Reine Angew. Math. 213(1964), 187–199.Google Scholar