Hostname: page-component-77c89778f8-9q27g Total loading time: 0 Render date: 2024-07-18T02:59:58.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodicity of Clifford algebras and exact octagons of Witt groups

Published online by Cambridge University Press:  24 October 2008

D. W. Lewis
D. W. Lewis
Affiliation:
Department of Mathematics, University College Dublin
Get access Rights & Permissions [Opens in a new window]

Extract

Exact octagons, i.e. circular eight-term exact sequences, have cropped up recently in a few places in the literature. Papers of the author [11], and implicitly [10], the book of M. Warshauer[14], and the notes [5], all contain exact octagons. The first three references involve octagons of Witt groups of quadratic and other kinds of forms, the last reference extending the octagons to the setting of L-groups, i.e. surgery obstruction groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 263 - 269
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Atiyah, M. F., Bott, R. and Shapiro, A.. Clifford modules. Topology 3 (suppl. 1) (1964), 3–38.CrossRefGoogle Scholar
[2]Edwards, B. H.. A note on Clifford algebra periodicity. Rev. Un. Mat. Argentina 28 (1977), 155–160.Google Scholar
[3]Frohlich, A.. Orthogonal and symplectic representations of groups. Proc. London Math. Soc. 24 (1972), 470–506.CrossRefGoogle Scholar
[4]Frohlich, A. and McEvett, A. M.. Forms over rings with involution. J. Algebra 12 (1969), 79–104.CrossRefGoogle Scholar
[5]Hambleton, I., Taylor, L. and Williams, B.. An introduction to maps between surgery obstruction groups. In Algebraic Topology (Aarhus, 1982), Lecture Notes in Math. vol. 1051 (Springer-Verlag, 1984), 49–127.Google Scholar
[6]Jacobson, N.. Basic Algebra, vol. II (Freeman, 1980).Google Scholar
[7]Karoubi, M.. Algébres de Clifford et K-théorie. Ann. Scient. Ecole Norm. Sup. 1 (1968), 161–270.CrossRefGoogle Scholar
[8]Lam, T. Y.. The Algebraic Theory of Quadratic Forms (Benjamin, 1973).Google Scholar
[9]Lewis, D. W.. Forms over real algebras and the multi-signature of a manifold. Adv. in Math. (1977), 272–284.CrossRefGoogle Scholar
[10]Lewis, D. W.. New improved exact sequences of Witt groups. J. Algebra 74 (1982), 206–210.CrossRefGoogle Scholar
[11]Lewis, D. W.. Exact sequences of Witt groups of equivariant forms. L'Enseign. Math. 29 (1983), 45–51.Google Scholar
[12]Micali, A. and Villamayor, O.. Sur les algébres de Clifford. Ann. Scient. Ecole Norm. Sup. 1 (1968), 271–304.CrossRefGoogle Scholar
[13]Pobteous, I. R.. Topological Geometry (Van Nostrand, 1969).Google Scholar
[14]Wabshauer, M. L.. The Witt Group of Degree k Maps and Asymmetric Inner Product Spaces, Lecture Notes in Math. vol. 914 (Springer-Verlag, 1982).CrossRefGoogle Scholar