Quasi-triangular, factorizable anti-dendriform bialgebras and relative Rota-Baxter operators

Abstract

We introduce the 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.

Theorems & Definitions (64)

• Definition 2.1
• Proposition 2.2
• Definition 2.3
• Remark 2.4
• Theorem 2.5
• Definition 2.6
• Theorem 2.7
• Definition 3.1
• Lemma 3.2
• proof