Jose Nicanor ALONSO ALVAREZ, Jose Manuel FERNANDEZ VILABOA, Ramon GONZALEZ RODRIGUEZ

Multiplication alteration by two-cocycles for bialgebras with weak antipode

In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weakantipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special caseof the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.

PDF

___

[1] Aizawa Y, Isaac PS. Weak Hopf algebras corresponding to Uq[sln] . Journal of Mathematical Physics 2003; 44: 5250-5267.
[2] Böhm G, Nill F, Szlachányi K. Weak Hopf algebras, I: Integral theory and C -structures. Journal of Algebra 1999; 221: 385-438.
[3] Doi Y. Braided bialgebras and quadratic bialgebras. Communications in Algebra 1993; 21: 1731-1749.
[4] Doi Y, Takeuchi M. Multiplication alteration by two-cocycles. The quantum version. Communications in Algebra 1994; 22: 5175-5732.
[5] Drinfeld VG. Quantum groups. In: Proceedings ICM. Berkeley, 1986, pp. 798-820.
[6] Hong Y, Li F. Weak Hopf algebras corresponding to quantum algebras Uq(f(K;H)) . Arabian Journal of Mathematics 2012; 1: 195-218.
[7] Kassel C. Quantum Groups. New York, NY, USA: Springer-Verlag, 1995.
[8] Li F. Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation. Journal of Algebra 1998; 208: 72-100.
[9] Li F. On quasi-bicrossed products of weak Hopf algebras. Acta Mathematica Sinica, English Series 2004; 20 (2): 305-318.
[10] Li F, Duplij S. Weak Hopf algebras and singular solutions of quantum Yang-Baxter equation. Communications in Mathematical Physics 2002; 225: 191-217.
[11] Majid S. Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction. Journal of Algebra 1990; 130: 17-64.
[12] Majid S. Quasitriangular Hopf algebras and Yang-Baxter equations. International Journal of Modern Physics A 1990; 5: 1-91.
[13] Majid S. Foundations of Quantum Group Theory. Cambridgei UK: Cambridge University Press, 1995.
[14] Radford DE. Minimal quasitriangular Hopf algebras. Journal of Algebra 1993; 157: 285-315.
[15] Rosenberg A, Zelinsky D. On Amitsur’s complex. Transactions of the American Mathematical Society 1960; 97: 327-356.
[16] Sweedler ME. Hopf Algebras. New York, NY, USA: Benjamin, 1969.
[17] Sweedler ME. Multiplication alteration by two-cocycles. Illinois Journal of Mathematics 1971; 15: 302-323.