2025/07/02 by Sun, Qinxiu, Wu, Min · 1 citation
#16T10 #17A30 #17A36 #17B38 #17B40 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2507.01650
We introduce a notion of quasi-triangular anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti-dendriform bialgebra leads to a factorization of the underlying anti-dendriform algebra. Moreover, relative Rota-Baxter operators with weights are introduced to characterize the solutions of the AD-YBE whose symmetric parts are invariant. Finally, we interpret factorizable anti-dendriform bialgebras in terms of quadratic Rota-Baxter anti-dendriform algebras.