O‘zbekiston matematika jurnali Ҷилди 70 № 2 (2026) · Саҳифаҳои 174-186
Anti-associative dendriform algebras
Normatov, Zafar
Аннотатсия
The general operadic approach to splitting algebraic operations was developed in [1]. By splitting the product in a given algebraic variety $\mathcal{C}$, notion of $\mathcal{C}$-dendriform algebras was systematically studied in[2]. 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 $\mathcal{O}$-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.
Lie algebra, pre-Lie algebra, dendriform algebra, Jacobi-Jordan algebra, pre-Jacobi-Jordan algebra, $\mathcal O$-operator
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