Multiplication alteration by two-cocycles. The nonassociative version
Abstract
In this paper we introduce the theory of multiplication alteration by two-cocycles for nonassociative structures like nonassociative bimonoids with left (right) division. Also we explore the connections between Yetter-Drinfeld modules for Hopf quasigroups, projections of Hopf quasigroups, skew pairings, and quasitriangular structures, obtaining the nonassociative version of the main results proved by Doi and Takeuchi for Hopf algebras.
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