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A generalization for \(n\)-cocycles. (English) Zbl 1261.16032

Summary: We give generalized definitions called type II \(n\)-cocycles and weak quasi-bialgebra and also show properties of type II \(n\)-cocycles and some results about weak quasi-bialgebras, for instance, construct a new structure of tensor product algebra over a module algebra on weak quasi-bialgebras.

MSC:

16T10 Bialgebras
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References:

[1] S. Majid, Foundations of Quantum Group Theory, Cambridge University Press, Cambridge, UK, 1995. · Zbl 0942.81576 · doi:10.1017/CBO9780511613104
[2] V. G. Drinfel’d, “Quasi-Hopf algebras,” Leningrad Mathematical Journal, vol. 1, no. 6, pp. 1419-1457, 1989. · Zbl 0718.16033
[3] D. Bulacu, F. Panaite, and F. Van Oystaeyen, “Quasi-Hopf algebra actions and smash products,” Communications in Algebra, vol. 28, no. 2, pp. 631-651, 2000. · Zbl 0953.16033 · doi:10.1080/00927870008826849
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