Extending structures for left-symmetric bialgebras

Abstract

We introduce the concept of braided left-symmetric bialgebras and construct cocycle bicrossproduct left-symmetric bialgebras. As an application, we solve the extending problem for left-symmetric bialgebras by using some non-abelian cohomology theory.

arXiv comment51 pages, some words and typos are modified. Continues arXiv:2112.11977, arXiv:2208.02221, and arXiv:2208.08281. arXiv admin note: substantial text overlap with arXiv:2203.15692