Book Review
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MathSciNet review:
1568154
Full text of review:
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This review is available free of charge.
Book Information:
Author:
S. Montgomery
Title:
Hopf algebras and their actions on rings
Additional book information:
CBMS Regional Conference Series in Mathematics, vol.\ 82, American Mathematical Society, Providence, RI, 1993, xiv\,+\,238 pp., US$32.00. ISBN 0-8218-0738-2.
Eiichi Abe, Hopf algebras, Cambridge Tracts in Mathematics, vol. 74, Cambridge University Press, Cambridge-New York, 1980. Translated from the Japanese by Hisae Kinoshita and Hiroko Tanaka. MR 594432
Yukio Doi and Mitsuhiro Takeuchi, Multiplication alteration by two-cocycles—the quantum version, Comm. Algebra 22 (1994), no. 14, 5715–5732. MR 1298746, DOI 10.1080/00927879408825158
Irving Kaplansky, Bialgebras, Lecture Notes in Mathematics, University of Chicago, Department of Mathematics, Chicago, Ill., 1975. MR 0435126
George Lusztig, Quantum groups at roots of $1$, Geom. Dedicata 35 (1990), no. 1-3, 89–113. MR 1066560, DOI 10.1007/BF00147341
Susan Montgomery, Duality for actions and coactions of groups, Group actions on rings (Brunswick, Maine, 1984) Contemp. Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985, pp. 191–207. MR 810652, DOI 10.1090/conm/043/810652
Donald S. Passman, Group rings, crossed products and Galois theory, CBMS Regional Conference Series in Mathematics, vol. 64, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. MR 840467
Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
- [A]
- E. Abe, Hopf algebras, Cambridge Univ. Press, Cambridge, 1980. MR 594432 (83a:16010)
- [DT]
- Y. Doi and M. Takeuchi, Multiplication alteration by two-cocycles--The quantum version, Comm. Algebra (to appear). MR 1298746 (95j:16043)
- [K]
- I. Kaplansky, Bialgebras, Lecture Notes in Math., Univ. of Chicago, Chicago, IL, 1975. MR 0435126 (55:8087)
- [L]
- G. Lusztig, Quantum groups at roots of 1, Geom. Dedicata 35 (1990), 89-114. MR 1066560 (91j:17018)
- [M]
- S. Montgomery, ed., Group actions on rings, Contemp. Math., vol. 43, Amer. Math. Soc., Providence, RI, 1985. MR 810652 (87h:16048)
- [P]
- D. Passman, Group rings, crossed products and Galois theory, CBMS Regional Conf. Ser. in Math., vol. 64, Amer. Math. Soc., Providence, RI, 1986. MR 840467 (87e:16033)
- [S]
- M. Sweedler, Hopf algebras, Benjamin, New York, 1969. MR 0252485 (40:5705)
Review Information:
Reviewer:
Mitsuhiro Takeuchi
Journal:
Bull. Amer. Math. Soc.
32 (1995), 125-127
DOI:
https://doi.org/10.1090/S0273-0979-1995-00549-5
