DG (co)algebras, DG Lie algebras and L∞ algebras
نویسنده
چکیده
منابع مشابه
An explicit construction of the Quillen homotopical category of dg Lie algebras
Let g1 and g2 be two dg Lie algebras, then it is well-known that the L∞ morphisms from g1 to g2 are in 1 − 1 correspondence to the solutions of the Maurer-Cartan equation in some dg Lie algebra k(g1, g2). Then the gauge action by exponents of the zero degree component k(g1, g2) 0 on MC ⊂ k(g1, g2) 1 gives an explicit ”homotopy relation” between two L∞ morphisms. We prove that the quotient categ...
متن کاملDomenico Fiorenza And
We show that the mapping cone of a morphism of differential graded Lie algebras χ : L → M can be canonically endowed with an L∞-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L∞-algebras. The associated deformation functor coincides with the one introduced by t...
متن کاملThe structure of a pair of nilpotent Lie algebras
Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...
متن کاملDeformation of Singularities via L∞-Algebras
This is an addendum to the paper “Deformation of L∞-Algebras” [9]. We explain in which way the deformation theory of L∞-algebras extends the deformation theory of singularities. We show that the construction of semi-universal deformations of L∞-algebras gives explicit formal semiuniversal deformations of isolated singularities. Introduction In this paper, we apply the following general idea for...
متن کاملOn dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کامل