Bialgebra structures of 2-associative algebras
Rings and Algebras
2008-09-09 v1 Quantum Algebra
Abstract
This work is devoted to study 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 an associative algebra and the classification of these structures in low dimensions.
Cite
@article{arxiv.0809.1144,
title = {Bialgebra structures of 2-associative algebras},
author = {Khadra Dekkar and Abdenacer Makhlouf},
journal= {arXiv preprint arXiv:0809.1144},
year = {2008}
}