Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 03 Aug 2020 12:34:36 GMT2020-08-03T12:34:36Z5051A New Approach to Leibniz Bialgebrashttp://hdl.handle.net/10316/43767Title: A New Approach to Leibniz Bialgebras
Authors: Barreiro, Elisabete; Benayadi, Saïd
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.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/437672015-01-01T00:00:00ZHomogeneous Symmetric Antiassociative Quasialgebrashttp://hdl.handle.net/10316/43825Title: Homogeneous Symmetric Antiassociative Quasialgebras
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: Our main purpose is to provide for homogeneous (even or odd) symmetric antiassociative quasialgebras a structure theory analogous to that for homogeneous symmetric associative superalgebras given in [5] and to present an inductive description of these classes of algebras.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/438252014-01-01T00:00:00ZOdd-quadratic Lie superalgebrashttp://hdl.handle.net/10316/11303Title: Odd-quadratic Lie superalgebras
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: An odd-quadratic Lie superalgebra is a Lie superalgebra with a nondegenerate
supersymmetric odd invariant bilinear form. In this paper we give examples
and present some properties of odd-quadratic Lie superalgebras, introduce the
notions of double extension and generalized double extension of odd-quadratic Lie
superalgebras and give an inductive classi cation of odd-quadratic Lie superalgebras
such that the even part is a reductive Lie algebra
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113032007-01-01T00:00:00ZQuadratic Lie superalgebras with reductive even parthttp://hdl.handle.net/10316/11304Title: Quadratic Lie superalgebras with reductive even part
Authors: Albuquerque, Helena; Barreiro, Elisabete; Benayadi, Saïd
Abstract: The aim of this paper is to exibit some non trivial examples of quadratic
Lie superalgebras such that the even part is a reductive Lie algebra and the action
of the even part on the odd part is not completely reducible and to give an inductive
classi cation of this class of quadratic Lie superalgebras. The notion of generalized
double extension of quadratic Lie superalgebras proposed by I. Bajo, S. Benayadi
and M. Bordemann [1] has a crucial importance in this work. In particular we will
improve some results of [4], in the sense that we will not demand that the action of
the even part on the odd part is completely reducible, which naturally makes the
proofs of our results more diffcult.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113042007-01-01T00:00:00ZThe structure of Leibniz superalgebras admitting a multiplicative basishttp://hdl.handle.net/10316/43773Title: The structure of Leibniz superalgebras admitting a multiplicative basis
Authors: Albuquerque, Helena; Barreiro, Elisabete; Calderón Martín, Antonio J.; Sánchez Delgado, José María
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/437732016-01-01T00:00:00Z