2020/10/18 by Mafoya Landry Dassoundo, Dassoundo, Mafoya Landry
Mathematics · #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2011.05172
Pre-anti-flexible family algebras are introduced and linked with the notions\nof relative anti-flexible algebras, left and right pre-Lie family algebras and\nrelative Lie algebras which are for mostly newly defined. Relative\npre-anti-flexible algebras are given and their underlying algebras structures\nsuch as pre-anti-flexible family algebras, left and right pre-Lie family\nalgebras, and other are investigated and significant identities linking those\nintroduced structures are derived. In addition, a generalization of the\nRota-Baxter operators defined on a relative anti-flexible algebra is introduced\nand both Rota-Baxter operators and its generalization are used to build\nrelative pre-anti-flexible algebras structures underlying relative\nanti-flexible algebras and related consequences are derived.\n