In this paper we introduce the theory of multiplication alteration by two-cocycles for bialgebras with weak antipode. Moreover, by the connection between two-cocycles and invertible skew pairings, we show that a special case of the double cross product of these bialgebras can be obtained as a deformation of a bialgebra with weak antipode.
ALONSO, JOSE NICANOR; VILABOA, JOSÉ MANUEL FERNANDEZ; and RODRIGUEZ, RAMON GONZALEZ
"Multiplication alteration by two-cocycles for bialgebras with weak antipode,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 11.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/11