Related papers: On the Lie algebras of surface pure braid groups
This paper develops the structure theory of a Malcev algebra via the consideration of its most important and largest Lie (sub-) algebra. We introduce the notion of a Lie algebra which uniquely corresponds to a Malcev algebra and use this…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
We determine the lower central series and corresponding residual properties for braid groups and pure braid groups of orientable surfaces.
We will define and study some generalisations of pure $\mathfrak{g}$-braid groups that occur in the theory of connections on curves, for any complex reductive Lie algebra $\mathfrak{g}$. They make up local pieces of the wild mapping class…
The Recognition Theorem for graded Lie algebras is an essential ingredient in the classification of finite-dimensional simple Lie algebras over an algebraically closed field of characteristic p > 3. The main goal of this monograph is to…
We classify a class of infinite-dimensional simple graded pre-Lie algebras on the graded vector space underlying the algebra of Laurent polynomials, with a specific form for the product.
It is shown that the Zassenhaus restricted $\mathbb F_p$-Lie algebra of a (pro-p) group G can be presented by the Magnus Lie algebra of G. For the class of (pro-p) groups for which the terms of the lower central series are torsion-free, the…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
The purpose of this paper is twofold. Firstly, to emphasise that the class of Lie algebras with chain lattices of ideals are elementary blocks in the embedding or decomposition of Lie algebras with finite lattice of ideals. Secondly, to…
We introduce a representation theory of q-Lie algebras defined earlier in \cite{DG1}, \cite{DG2}, formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in…
Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each…
We describe the lower algebraic $K$-theory of the integral group ring of both the pure and full braid groups of the real projective plane $\mathbb{R}P^2$ with $3$ strings, as well as that of the integral group ring of the mapping class…
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
This is an expository article on representation theory of toroidal Lie algebras. We summerize all the results on representation theory of toroidal Lie algebras obtained in the last fifteen years. Apart from that a natural genaralization of…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
Lie brackets or Lie affgebra structures on several classes of affine spaces of matrices are studied. These include general normalised affine matrices, special normalised affine matrices, anti-symmetric and anti-hermitian normalised affine…
Derived brackets provide a mechanism for generating algebraic structures from graded Lie superalgebras, with applications in Poisson geometry, mathematical physics, and the theory of algebroids. In this paper, we present a complete…
Goldman (Invent. Math. 85(2) (1986) 263) and Turaev (Ann. Sci. Ecole Norm. Sup. (4) 24 (6)(1991) 635) found a Lie bialgebra structure on the vector space generated by non-trivial free homotopy classes of loops on an orientable surface. Chas…
Loday's dendriform algebras and its siblings pre-Lie and zinbiel have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each individual…