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Book Review
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Book Information
Author(s):
Martin Lorenz
Title:
Multiplicative invariant theory
Additional book information:
Encyclopaedia of Mathematical Sciences, vol. 135, Invariant Theory and Algebraic Transformation Groups, VI,
Springer-Verlag, Berlin,
2005,
xii+177,
US$109.00,
ISBN 3-540-24323-2
References:
-
- [Be]
- George M. Bergman, The logarithmic limit-set of an algebraic variety, Trans. Amer. Math. Soc. 157 (1971), 459-469. MR 0280489 (43:6209)
- [BL]
- Christine Bessenrodt and Lieven Le Bruyn, Stable rationality of certain
-quotients, Invent. Math. 104 (1991), no. 1, 179-199. MR 1094051 (92m:14060) - [Bo]
- N. Bourbaki, Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968. MR 0240238 (39:1590)
- [DM]
- Frank DeMeyer and Thomas McKenzie, On generic polynomials, J. Algebra 261 (2003), no. 2, 327-333. MR 1966633 (2003m:12007)
- [Fa1]
- Daniel R. Farkas, Multiplicative invariants, Enseign. Math. (2) 30 (1984), nos. 1-2, 141-157. MR 0743674 (85h:16042)
- [Fa2]
- -, Toward multiplicative invariant theory, in ``Group Actions on Rings'' (Brunswick, Maine, 1984), 69-80, Contemp. Math. 43, Amer. Math. Soc., Providence, RI, 1985. MR 0810644 (87b:16013)
- [Fa3]
- -, Reflection groups and multiplicative invariants, Rocky Mountain J. Math. 16 (1986), no. 2, 215-222. MR 0843049 (87k:20085)
- [Fo1]
- Edward Formanek, The center of the ring of
generic matrices, Linear and Multilinear Algebra 7 (1979), no. 3, 203-212. MR 0540954 (80h:16019) - [Fo2]
- -, The center of the ring of
generic matrices, J. Algebra 62 (1980), no. 2, 304-319. MR 0563230 (81g:15032) - [Jo]
- Camille Jordan, Mémoire sur l'équivalence des formes, J. École Polytech. 48 (1880), 112-150.
- [Ka]
- Ming-Chang Kang, Picard groups of some rings of invariants, J. Algebra 58 (1979), no. 2, 455-461. MR 0540650 (82m:14004)
- [Lm]
- Nicole Lemire, Reduction in the rationality problem for multiplicative invariant fields, J. Algebra 238 (2001), no. 1, 51-81. MR 1822183 (2002b:13009)
- [Ln]
- H. W. Lenstra Jr., Rational functions invariant under a finite abelian group, Invent. Math. 25 (1974), 299-325. MR 0347788 (50:289)
- [Lo1]
- Martin Lorenz, Class groups of multiplicative invariants, J. Algebra 177 (1995), no. 1, 242-254. MR 1356370 (96j:16036)
- [Lo2]
- -, Picard groups of multiplicative invariants, Comment. Math. Helv. 72 (1997), no. 3, 389-399. MR 1476055 (98m:13019)
- [Lo3]
- -, On the Cohen-Macaulay property of multiplicative invariants, Trans. Amer. Math. Soc. 358 (2006), no. 4, 1605-1617. MR 2186988
- [Pr1]
- Claudio Procesi, Non-commutative affine rings, Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I (8) 8 (1967), 237-255. MR 0224657 (37:256)
- [Pr2]
- -, The invariant theory of
matrices, Advances in Math. 19 (1976), no. 3, 306-381. MR 0419491 (54:7512) - [Ro]
- J. E. Roseblade, Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. (3) 36 (1978), no. 3, 385-447. MR 0491797 (58:10996a)
- [Sa1]
- David J. Saltman, Generic Galois extensions and problems in field theory, Adv. in Math. 43 (1982), no. 3, 250-283. MR 0648801 (84a:13007)
- [Sa2]
- -, Retract rational fields and cyclic Galois extensions, Israel J. Math. 47 (1984), nos. 2-3, 165-215. MR 0738167 (85j:13008)
- [ST]
- G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6 (1954), 274-304. MR 0059914 (15:600b)
- [St]
- Robert Steinberg, On a theorem of Pittie, Topology 14 (1975), 173-177. MR 0372897 (51:9101)
- [Sy]
- J. J. Sylvester, On the involution of two matrices of the second order, British Assoc. Report (Southport) (1883), 430-432. Reprinted in: ``Collected Mathematical Papers'', Vol. 4, Chelsea, 1973, pp. 115-117.
Additional Information:
Reviewer(s):
D.
S.
Passman
Affiliation:
University of Wisconsin, Madison
Email:
passman@math.wisc.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
44
(2007),
157-162.
MSC
(2000):
Primary 13A50, 16S34, 16W22, 20F55.
PII:
S 0273-0979(06)01122-0
Posted:
August 28, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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