Bialgebra structures of 2-associative algebras

Details Bialgebra structures of 2-associative algebras Bialgebra structures of 2-associative algebras

2008-09-06

arxiv.org/abs/0809.1144v1

Mathematics

Rings and Algebras

Scientific paper

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.

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