LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Anti-flexible bialgebras

Photo from wikipedia

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The… Click to show full abstract

We establish a bialgebra theory for anti-flexible algebras in this paper. We introduce the notion of an anti-flexible bialgebra which is equivalent to a Manin triple of anti-flexible algebras. The study of a special case of anti-flexible bialgebras leads to the introduction of anti-flexible Yang–Baxter equation in an anti-flexible algebra which is an analogue of the classical Yang–Baxter equation in a Lie algebra or the associative Yang–Baxter equation in an associative algebra. It is unexpected consequence that both the anti-flexible Yang–Baxter equation and the associative Yang–Baxter equation have the same form. A skew-symmetric solution of anti-flexible Yang–Baxter equation gives an anti-flexible bialgebra. Finally the notions of an [Formula: see text]-operator of an anti-flexible algebra and a pre-anti-flexible algebra are introduced to construct skew-symmetric solutions of anti-flexible Yang–Baxter equation.

Keywords: anti flexible; baxter equation; yang baxter; anti

Journal Title: Journal of Algebra and Its Applications
Year Published: 2021

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.