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Non-Isomorphic Equivalent Azumaya Algebras

Published online by Cambridge University Press:  20 November 2018

Lindsay N. Childs
Lindsay N. Childs*
Affiliation:
Department of Mathematics and Statistics State University of New York at Albany Albany, NY 12222
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Abstract

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We explicitly describe an infinite collection of pairs of Azumaya algebras over the ring of integers of real quadratic number fields K which are maximal orders in the usual quaternion algebra over K, hence Brauer equivalent, but are not isomorphic. The result follows from an identification of the groups of norm one units, using the classification of Coxeter.

Keywords

16A1616A18
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 340 - 343
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Chase, S.U., Harrison, D.K., Rosenberg, A., Galois theory and Galois cohomology of commutative rings. Memoirs Amer. Math. Soc. 52 (1965), pp. 15–33.Google Scholar
2. Chase, S.U., Sweedler, M.E., Hopf Algebras and Galois Theory. Springer Lecture Notes in Mathematics 97 (1968).Google Scholar
3. Childs, L.N., DeMeyer, F.R., On automorphism of separable algebras. Pacific J. Math. 23 (1967), pp. 25–34.Google Scholar
4. Childs, L.N., On projective modules and automorphisms of central separable algebras. Canad. J. Math. 21 (1969), pp. 44–53.Google Scholar
5. Childs, L.N., Azumaya algebras which are not smash products. Rocky Mount. J. (to appear).Google Scholar
6. Coxeter, H.S.M., The binary polyhedral groups and other generalizations of quaternion groups. Duke Math. J. 7 (1940), pp. 367–379.Google Scholar
7. Eichler, M., Uber die Idealklassenzahl total definiter Quaternionalgebren. Math. Z. 43 (1937), pp. 102–109.Google Scholar
8. Gamst, J., Hoechsmann, K., Quaternions generalises. C.R. Acad. Sci. Paris 269 (1969), pp. 560—562.Google Scholar
9. Hammond, W.F., The Hilbert modular surface of a real quadratic field. Math. Ann. 200 (1973), pp. 25–45.Google Scholar
10. Swan, R.G., Projective modules over group rings and maximal orders. Annals of Math. 76 (1962), pp. 55–61.Google Scholar
11. Vigneras, M.-F., Arithmétique des Algebras de Quaternions. Springer LNM 800 (1980).Google Scholar