Geodesic
Division Graded Algebras in the Brauer-Wall Group
Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 21-24

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1996-003-2
Mots-clés : 13A20, graded algebra, division algebra, Brauer-Wall group 
Coghlan, Francis; Hoffman, Peter. Division Graded Algebras in the Brauer-Wall Group. Canadian mathematical bulletin, Tome 39 (1996) no. 1, pp. 21-24. doi: 10.4153/CMB-1996-003-2
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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

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