Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43767
Title: A New Approach to Leibniz Bialgebras
Authors: Barreiro, Elisabete 
Benayadi, Saïd 
Issue Date: 2015
Publisher: Springer
Project: UID/MAT/00324/2013 
Serial title, monograph or event: Algebras and Representation Theory
Volume: 19
Issue: 1
Abstract: A study of Leibniz bialgebras arising naturally through the double of Leibniz algebras analogue to the classical Drinfeld’s double is presented. A key ingredient of our work is the fact that the underline vector space of a Leibniz algebra becomes a Lie algebra and also a commutative associative algebra, when provided with appropriate new products. A special class of them, the coboundary Leibniz bialgebras, gives us the natural framework for studying the Yang-Baxter equation (YBE) in our context, inspired in the classical Yang-Baxter equation as well as in the associative Yang-Baxter equation. Results of the existence of coboundary Leibniz bialgebra on a symmetric Leibniz algebra under certain conditions are obtained. Some interesting examples of coboundary Leibniz bialgebras are also included. The final part of the paper is dedicated to coboundary Leibniz bialgebra structures on quadratic Leibniz algebras.
URI: http://hdl.handle.net/10316/43767
Other Identifiers: 10.1007/s10468-015-9563-6
DOI: 10.1007/s10468-015-9563-6
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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