A lower central series for split Hopf algebras with involution

Jordan, Bruce W.

doi:10.1090/S0002-9947-1980-0552268-0

A lower central series for split Hopf algebras with involution

Author: Bruce W. Jordan
Journal: Trans. Amer. Math. Soc. 257 (1980), 427-454
MSC: Primary 16A24; Secondary 57T05
DOI: https://doi.org/10.1090/S0002-9947-1980-0552268-0
MathSciNet review: 552268
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A lower central series is defined for split Hopf algebras with involution over a field k. Various structure theorems for coalgebras and Hopf algebras are established.

[1] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480
[2] P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 0072873, https://doi.org/10.1112/plms/s3-4.1.419
[3] Peter John Hilton and Urs Stammbach, A course in homological algebra, Springer-Verlag, New York-Berlin, 1971. Graduate Texts in Mathematics, Vol. 4. MR 0346025
[4] Jean-Michel Lemaire, Algèbres connexes et homologie des espaces de lacets, Lecture Notes in Mathematics, Vol. 422, Springer-Verlag, Berlin-New York, 1974 (French). MR 0370566
[5] John W. Milnor and John C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211–264. MR 174052, https://doi.org/10.2307/1970615
[6] John C. Moore and Larry Smith, Hopf algebras and multiplicative fibrations. I, Amer. J. Math. 90 (1968), 752–780. MR 234455, https://doi.org/10.2307/2373482
[7] Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
[8] Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581