${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation

Details ${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation ${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation

2009-09-21

arxiv.org/abs/0909.3740v1

Communications in Algebra 38 (2010) 4277-4321

Physics

Mathematical Physics

41pages, appear in Communications in Algebra

Scientific paper

We introduce notions of ${\mathcal O}$-operators of the Loday algebras including the dendriform algebras and quadri-algebras as a natural generalization of Rota-Baxter operators. The invertible $\mathcal O$-operators give a sufficient and necessary condition on the existence of the $2^{n+1}$ operations on an algebra with the $2^{n}$ operations in an associative cluster. The analogues of the classical Yang-Baxter equation in these algebras can be understood as the $\mathcal O$-operators associated to certain dual bimodules. As a byproduct, the constraint conditions (invariances) of nondegenerate bilinear forms on these algebras are given.

Affiliated with

Also associated with

No associations

Rating

${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with ${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and ${\mathcal O}$-operators of Loday algebras and analogues of the classical Yang-Baxter equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-432453