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Quartic Algebras

Published online by Cambridge University Press:  20 November 2018

Carla Farsi  and
Neil Watling
Carla Farsi
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 1A1
Neil Watling
Affiliation:
Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14214, U.S.A.
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Abstract

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In this paper we study the fixed point algebra of the automorphism of the rotation algebra , θ = p/q with p, q coprime positive integers, given by u → v-1, v → u. We give a general characterization of the fixed point algebra, determine its K-theory and consider the related crossed-product algebra ⋊Ƭ Z4.

Keywords

46L4046L0546L5546L80
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 6 , 01 December 1992 , pp. 1167 - 1191
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Apostol, T., Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer- Verlag, New-York, 1984.Google Scholar
2. Berndt, B.C. and Evans, R.J., The Determination of Gauss Sums, Bull. Amer. Math. Soc. 2(1981), 107–129.Google Scholar
3. Bratteli, O., Elliott, G.A., Evans, D.E. and Kishimoto, A., Non commutative spheres I, Int. Jour, of Math., 2(1991), 139–166.Google Scholar
4. Bratteli, O.,Non commutative spheres II, Rational Rotations, Jour, of Op. Th., to appear.Google Scholar
5. Farsi, C., K-theoretical index Theorems for orbifolds, Quat. J. Math. 43(1992), 183–200.Google Scholar
6. Farsi, C. and Watling, N., Irrational fixed point subalgebras I, preprint.Google Scholar
7. Farsi, C., Cubic algebras, preprint.Google Scholar
8. Farsi, C., Elliptic algebras, preprint.Google Scholar
9. Gauss, C.F., Summatio quarumdamserierumsingularium, Comm. soc. reg. sci. Gottingensis rec. 1( 1811 ).Google Scholar
10. Gauss, C.F., Werke, K. Gesell. Wiss., Göttingen, 1876.Google Scholar
11. Grosswald, E., Representations of integers as sums of squares, Springer-Verlag, New York, 1985.Google Scholar
12. Høegh-Krohn, R. and Skjelbred, T., Classification of C*-algebras admitting ergodic actions on the two dimensional torus, J. Reine Angewandte Math. 328(1981), 1–8.Google Scholar
13. Landau, E., Elementary Number Theory, 2nd edition, Chelsea Publishing Company, New York, 1966.Google Scholar
14. Narasimhan, R., Complex Analysis in one variable, Birkhauser, Boston, Basel, Stuttgard, 1985.Google Scholar
15. Rosenberg, J., Appendix to “Crossed products of UHF algebras by product type actions “, Duke Math. J. 46(1979), 25–26.Google Scholar