Anti-associative dendriform algebras
Abstract
The general operadic approach to splitting algebraic operations was developed in BBGN. By splitting the product in a given algebraic variety C, notion of C-dendriform algebras was systematically studied in OPV. This article aims to study ``anti-associative dendriform algebras", which offer an approach to addressing anti-associativity. These algebras are defined by two operations whose sum is anti-associative. Furthermore, the notion of O-operators on anti-associative algebras is presented as a tool to interpret anti-associative dendriform algebras. Moreover, anti-associative algebras with nondegenerate Connes cocycles admit compatible anti-associative dendriform algebra structures.
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