Book Review
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MathSciNet review:
1567340
Full text of review:
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Book Information:
Author:
Eiichi Abe
Title:
Hopf algebras
Additional book information:
Cambridge Univ. Press, 1980, translated by Hisae Kinoshita and Hiroko Tanaka, xii + 284 pp., $39.50.
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
Harry Prince Allen and Moss Eisenberg Sweedler, A theory of linear descent based upon Hopf algebraic techniques, J. Algebra 12 (1969), 242–294. MR 242906, DOI 10.1016/0021-8693(69)90051-9
Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
4. M. Demanzure and P. Gabriel, Groups algébriques, North-Holland, Amsterdam, 1970.
G. Hochschild, Algebraic Lie algebras and representative functions, Illinois J. Math. 3 (1959), 499–523. MR 125910
G. Hochschild, Algebraic Lie algebras and representative functions. Supplement, Illinois J. Math. 4 (1960), 609–618. MR 125911
G. Hochschild, Introduction to affine algebraic groups, Holden-Day, Inc., San Francisco, Calif.-Cambridge-Amsterdam, 1971. MR 0277535
G. Hochschild and G. D. Mostow, Representations and representative functions of Lie groups, Ann. of Math. (2) 66 (1957), 495–542. MR 98796, DOI 10.2307/1969906
David E. Radford, The order of the antipode of a finite dimensional Hopf algebra is finite, Amer. J. Math. 98 (1976), no. 2, 333–355. MR 407069, DOI 10.2307/2373888
John Brendan Sullivan, The uniqueness of integrals for Hopf algebras and some existence theorems of integrals for commutative Hopf algebras, J. Algebra 19 (1971), 426–440. MR 288167, DOI 10.1016/0021-8693(71)90100-1
Moss Eisenberg Sweedler, Cohomology of algebras over Hopf algebras, Trans. Amer. Math. Soc. 133 (1968), 205–239. MR 224684, DOI 10.1090/S0002-9947-1968-0224684-2
Moss Eisenberg Sweedler, Structure of inseparable extensions, Ann. of Math. (2) 87 (1968), 401–410. MR 223343, DOI 10.2307/1970711
Moss E. Sweedler, Groups of simple algebras, Inst. Hautes Études Sci. Publ. Math. 44 (1974), 79–189. MR 364332
Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
Mitsuhiro Takeuchi, Relative Hopf modules—equivalences and freeness criteria, J. Algebra 60 (1979), no. 2, 452–471. MR 549940, DOI 10.1016/0021-8693(79)90093-0
William C. Waterhouse, Antipodes and group-likes in finite Hopf algebras, J. Algebra 37 (1975), no. 2, 290–295. MR 379568, DOI 10.1016/0021-8693(75)90078-2
William C. Waterhouse, Introduction to affine group schemes, Graduate Texts in Mathematics, vol. 66, Springer-Verlag, New York-Berlin, 1979. MR 547117
David Winter, The structure of fields, Graduate Texts in Mathematics, No. 16, Springer-Verlag, New York-Heidelberg, 1974. MR 0389873
- 1.
- Eiichi Abe, Hopf algebras, Cambridge Univ. Press, Cambridge, 1980. MR 0594432
- 2.
- H. P. Allen and M. E. Sweedler, A theory of linear descent based upon Hopf algebraic techniques, J. Algebra 12 (1969), 242-294. MR 242906
- 3.
- Armand Borel, Linear algebraic groups, Benjamin, New York, 1969. MR 251042
- 4.
- M. Demanzure and P. Gabriel, Groups algébriques, North-Holland, Amsterdam, 1970.
- 5.
- Gerhard Hochschild, Algebraic Lie algebras and representative functions, Illinois J. Math. 3 (1959), 499-523. MR 125910
- 6.
- Gerhard Hochschild, Algebraic Lie algebras and representative functions. Supplement, Illinois J. Math. 4 (1960), 609-618. MR 125911
- 7.
- Gerhard Hochschild, Introduction to affine algebraic groups, Holden-Day, San Francisco, 1971. MR 277535
- 8.
- G. Hochschild and G. D. Mostow, Representations and representative functions of Lie groups, Ann. of Math. (2) 66 (1957), 495-547. MR 98796
- 9.
- David E. Radford, The order of the antipode of a finite dimensional Hopf algebra is finite. Amer. J. Math. 98 (1973), 333-355. MR 407069
- 10.
- John B. Sullivan, The uniqueness of integrals for Hopf algebras and some existence theorems of integrals for commutative Hopf algebras, J. Algebra 19 (1971), 426-440. MR 288167
- 11.
- Moss Sweedler, Cohomology of algebras over Hopf algebras, Trans. Amer. Math. Soc. 133 (1968), 205-239. MR 224684
- 12.
- Moss Sweedler, Structure of inseparable extensions, Ann. of Math. (2) 87 (1968), 401-410. Correction: Ann. of Math. (2) 89 (1969), 206-207. MR 223343
- 13.
- Moss Sweedler, Groups of simple algebras, Publ. Math. I. H. E. S. 44 (1975), 79-189. MR 364332
- 14.
- Moss Sweedler, Hopf algebras, Benjamin, New York, 1969. MR 252485
- 15.
- Mitsuhiro Takeuchi, Relative Hopf modules--equivalences and freeness criteria, J. Algebra 60 (1979), 452-471. MR 549940
- 16.
- William C. Waterhouse, Antipodes and group-likes in finite Hopf algebras, J. Algebra 37 (1975), 290-295. MR 379568
- 17.
- William C. Waterhouse, Introduction to affine group schemes, Springer-Verlag, New York, 1979. MR 547117
- 18.
- David J. Winter, The structure of fields, Springer-Verlag, New York, 1974. MR 389873
Review Information:
Reviewer:
Moss E. Sweedler
Journal:
Bull. Amer. Math. Soc.
5 (1981), 349-354
DOI:
https://doi.org/10.1090/S0273-0979-1981-14954-5
