Book Review
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Book Information:
Author:
A. J. Hahn
Title:
Quadratic algebras, Clifford algebras, and arithmetic Witt groups
Additional book information:
Springer-Verlag,
Berlin and New York,
1994,
xi+286 pp.,
ISBN 0-387-94110-X,
$34.00$
Jón Kr. Arason, Der Wittring projektiver Räume, Math. Ann. 253 (1980), no. 3, 205–212 (German). MR 597829, DOI 10.1007/BF03219998
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
J. J. Corliss, Upper limits to the real roots of a real algebraic equation, Amer. Math. Monthly 46 (1939), 334–338. MR 4
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
John E. Gilbert and Margaret A. M. Murray, Clifford algebras and Dirac operators in harmonic analysis, Cambridge Studies in Advanced Mathematics, vol. 26, Cambridge University Press, Cambridge, 1991. MR 1130821, DOI 10.1017/CBO9780511611582
Manfred Knebusch, Symmetric bilinear forms over algebraic varieties, Conference on Quadratic Forms—1976 (Proc. Conf., Queen’s Univ., Kingston, Ont., 1976) Queen’s Papers in Pure and Appl. Math., No. 46, Queen’s Univ., Kingston, Ont., 1977, pp. 103–283. MR 0498378
Max-Albert Knus, Quadratic and Hermitian forms over rings, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 294, Springer-Verlag, Berlin, 1991. With a foreword by I. Bertuccioni. MR 1096299, DOI 10.1007/978-3-642-75401-2
H. Blaine Lawson Jr. and Marie-Louise Michelsohn, Spin geometry, Princeton Mathematical Series, vol. 38, Princeton University Press, Princeton, NJ, 1989. MR 1031992
[Mc] A. McIntosh, review of Clifford Algebra and Spinor-valued Functions, 
by R. Delanghe, F. Sommen, and V. Sou\v{c}ek, Bull. Amer. Math. Soc. (N.S.) 32 (1995), 344--348.
A. S. Merkur′ev, On the norm residue symbol of degree $2$, Dokl. Akad. Nauk SSSR 261 (1981), no. 3, 542–547 (Russian). MR 638926
John Milnor, Algebraic $K$-theory and quadratic forms, Invent. Math. 9 (1969/70), 318–344. MR 260844, DOI 10.1007/BF01425486
M. Ojanguren, R. Parimala, and R. Sridharan, Symplectic bundles over affine surfaces, Comment. Math. Helv. 61 (1986), no. 3, 491–500. MR 860136, DOI 10.1007/BF02621929
R. Parimala and R. Sujatha, Witt group of hyperelliptic curves, Comment. Math. Helv. 65 (1990), no. 4, 559–580. MR 1078098, DOI 10.1007/BF02566626
R. Parimala and R. Sridharan, Nonsurjectivity of the Clifford invariant map, Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 1, 49–56. K. G. Ramanathan memorial issue. MR 1280057, DOI 10.1007/BF02830873
Albrecht Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. 1 (1966), 116–132 (German). MR 200270, DOI 10.1007/BF01389724
- [Ar]
- J. Kr. Arason, Der Wittring projektiver Räume, Math. Ann. 253 (1980), 205--212. MR 0597829
- [AEJ]
- J. Kr. Arason, R. Elman, and B. Jacob, On the Witt ring of elliptic curves, pp. 1--25 in K-Theory and Algebraic Geometry (B. Jacob and A. Rosenberg, eds.), Proc. Symp. Pure Math., vol. 58.2, Amer. Math. Soc., Providence, R. I., 1995. MR 1:327 286
- [A]
- C. Arf, Untersuchungen über quadratische Formen in Körpern der Charakteristik
, J. Reine Angew. Math. 183 (1941), 148--167. MR 4:237f
- [CTS]
- J. L. Colliot-Thélène and R. Sujatha, The unramified Witt group of real anisotropic quadrics, pp. 127--147 in K-Theory and Algebraic Geometry (B. Jacob and A. Rosenberg, eds.), Proc. Symp. Pure Math., vol. 58.2, Amer. Math. Soc., Providence, R. I., 1995. MR 1:327 294
- [GM]
- J. Gilbert and M. Murray, Clifford Algebras and Dirac Operators in Harmonic Analysis, Cambridge Univ. Press, Cambridge, England, 1991. MR 1130821
- [Kn]
- M. Knebusch, Symmetric bilinear forms over algebraic varieties, pp. 103--283 in Conference on Quadratic Forms 1976 (G. Orzech, ed.), Queen's Papers in Pure and Applied Math., No. 46, Queen's Univ., Kingston, Ontario, 1977. MR 0498378
- [K]
- M.-A. Knus, Quadratic and Hermitian Forms over Rings, Springer-Verlag, Berlin, 1991. MR 1096299
- [LM]
- H.-B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, N.J., 1989. MR 1031992
- [Mc]
- A. McIntosh, review of Clifford Algebra and Spinor-valued Functions, by R. Delanghe, F. Sommen, and V. Sou\v{c}ek, Bull. Amer. Math. Soc. (N.S.) 32 (1995), 344--348.
- [M]
- A. S. Merkurjev, On the norm residue symbol of degree 2, Doklady Akad. Nauk. SSSR 261 (1981), 542--547; English trans. Soviet Math. Doklady, vol. 24, 1981, pp. 546--551. MR 0638926
- [Mi]
- J. Milnor, Algebraic
-theory and quadratic forms, Invent. Math. 9 (1970), 318--344. MR 0260844
- [OPS]
- M. Ojanguren, R. Parimala, and R. Sridharan, Symplectic bundles over affine surfaces, Comment. Math. Helv. 61 (1986), 491--500. MR 0860136
- [PSu]
- R. Parimala and R. Sujatha, Witt groups of hyperelliptic curves, Comment. Math. Helv. 65 (1990), 559--580. MR 1078098
- [PS]
- R. Parimala and R. Sridharan, Non-surjectivity of the Clifford invariant map, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 49--56. MR 1280057
- [P]
- A. Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. 1 (1966), 116--132. MR 0200270
Review Information:
Reviewer:
A. R. Wadsworth
Affiliation:
University of California, San Diego
Email:
arwadsworth@ucsd.edu
Journal:
Bull. Amer. Math. Soc.
33 (1996), 263-267
DOI:
https://doi.org/10.1090/S0273-0979-96-00645-3
Review copyright:
© Copyright 1996
American Mathematical Society
