Homotopy Leibniz algebras and derived brackets ( version 2 )
نویسنده
چکیده
We will give a generalized framework of derived bracket construction. The derived bracket construction provides a method of constructing homotopies. We will prove that a deformation derivation of dg Leibniz algebra (or called dg Loday algebra) induces a strong homotopy Leibniz algebra by the derived bracket method.
منابع مشابه
Homotopy Leibniz Algebras and Derived Brackets
We will discuss a bar/coalgebra construction of strong homotopy Leibniz algebras. We will give a generalized framework of derived bracket construction. We will prove that a deformation derivation of differential graded Leibniz algebra induces a strong homotopy Leibniz algebra by derived bracket method.
متن کاملDerived brackets and sh Leibniz algebras
We will give a generalized framework of derived bracket construction. It will be shown that a deformation differential provides a strong homotopy (sh) Leibniz algebra structure by derived bracket construction. A relationship between the three concepts, homotopy algebra theory, deformation theory and derived bracket construction, will be discussed. We will prove that the derived bracket construc...
متن کامل6 v 5 4 O ct 2 00 6 Non - Commutative Batalin - Vilkovisky Algebras , Homotopy Lie Algebras and the Courant Bracket
We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent ∆ operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie br...
متن کاملOn the Infinity Category of Homotopy Leibniz Algebras
We discuss various concepts of ∞-homotopies, as well as the relations between them (focussing on the Leibniz type). In particular ∞-n-homotopies appear as the n-simplices of the nerve of a complete Lie ∞-algebra. In the nilpotent case, this nerve is known to be a Kan complex [Get09]. We argue that there is a quasi-category of ∞-algebras and show that for truncated ∞-algebras, i.e. categorified ...
متن کاملHomotopy Lie Algebras and the Courant Bracket
We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent ∆ operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie br...
متن کامل