Baues cofibration for quadratic modules of Lie algebras

Abstract

In this paper; free quadratic modules and totally free objects in the category of quadratic modules are constructed over Lie algebras. We use the free quadratic modules of Lie algebras to show that the category of quadratic module of Lie algebras is a co…bration category by means of Baues.

Quadratic Modules of Lie Algebras Fibred Over Nil(2)-Modules of Lie Algebras

“…Definition 2.1. [13] The diagram of Lie algebra homomorphisms 2)-module of Lie algebras and the quotient map…”

“…Lie algebraic variation of a quadratic module is given by Ulualan and Uslu in [10]. Baues cofibration for a quadratic module of Lie algebra defined in [13]. The relations amongsimplicial Lie algebras and 2-crossed modules are given in [8] by using simplicial properties.…”

Finite coproducts in the category of quadratic modules of Lie algebras

“…In this study, we focus on quadratic modules of Lie algebras, one of the algebraic 3-type model, developed by Baues for group case, and whose homotopy structure is defined [22]. The Lie algebra version of this model was introduced in the [23] studied by Ulualan and Uslu, while the studies in [24,25] rely on quadratic module of commutative algebras. A different homotopy relation for quadratic modules of Lie algebras is constructed in [26,27].…”