Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 27 Nov 2022 19:15:31 GMT2022-11-27T19:15:31Z5021Odd-quadratic Lie superalgebras with a weak filiform module as an odd parthttp://hdl.handle.net/10316/100188Title: Odd-quadratic Lie superalgebras with a weak filiform module as an odd part
Authors: Barreiro, Elisabete; Benayadi, Saïd; Navarro, Rosa M.; Sánchez, José M.
Abstract: The aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that is a weak filiform -module (weak filiform type). We introduce this concept after having proved that the unique non-zero odd-quadratic Lie superalgebra with a filiform -module is the abelian 2-dimensional Lie superalgebra such that . Let us note that in this context the role of the center of is crucial. Thus, we obtain an inductive description of odd-quadratic Lie superalgebras of weak filiform type via generalized odd double extensions. Moreover, we obtain the classification, up to isomorphism, for the smallest possible dimensions, that is, six and eight.
Sat, 01 Jan 2022 00:00:00 GMThttp://hdl.handle.net/10316/1001882022-01-01T00:00:00ZThe structure of split regular BiHom-Lie algebrashttp://hdl.handle.net/10316/43819Title: The structure of split regular BiHom-Lie algebras
Authors: Calderón, Antonio J.; Sánchez, José M.
Abstract: We introduce the class of split regular BiHom-Lie algebras as the natural extension of the one of split Hom-Lie algebras and so of split Lie algebras. We show that an arbitrary split regular BiHom-Lie algebra L is of the form L = U +∑_j I_j with U a linear subspace of a fixed maximal abelian subalgebra H and any I_j a well described (split) ideal of L, satisfying [I_j ; I_k] = 0 if j ≠ k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its simple
ideals.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/438192016-01-01T00:00:00Z