Bialgebra structures of 2-associative algebras

الملخص EN

This work is devoted to the study of new bialgebra structures related to 2-associative algebras.

A 2-associative algebra is a vector space equipped with two associative multiplications.

We discuss the notions of 2-associative bialgebras, 2-bialgebras, and 2-2-bialgebras.

The first structure was revealed by J.-L.

Loday and M.

Ronco in an analogue of a Cartier-Milnor-Moore theorem, the second was suggested by Loday, and the third is a variation of the second one.

The main results of this paper are the construction of 2-associative bialgebras, 2-bialgebras, and 2-2-bialgebras starting from any associative algebra and the classification of these structures in low dimensions.