Related papers: Graphs and and two-step nilpotent Lie algebras
We show that the isomorphism class of a two-step solvable Lie poset subalgebra of a semisimple Lie algebra is determined by its dimension. We further establish that all such algebras are absolutely rigid.
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational…
A vertex with neighbours of degrees $d_1 \geq ... \geq d_r$ has {\em vertex type} $(d_1, ..., d_r)$. A graph is {\em vertex-oblique} if each vertex has a distinct vertex-type. While no graph can have distinct degrees, Schreyer, Walther and…
We establish a sharpening of Kirillov's lemma on nilpotent Lie algebras with 1-dimensional center and use it to study the structure of 3-step nilpotent Lie algebras.
In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether the algebra admits an idempotent or a pseudo-idempotent. We study the multiplicative…
We review the known results about characteristically nilpotent complex Lie algebras, as well as we comment recent developements in the theory.
Given a nilpotent Lie algebra $\mathfrak n$ we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the Lie algebra cohomology of $\mathfrak n$. The limit of this…
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for…
Every Lie algebra over a field $E$ gives rise to new Lie algebras over any subfield $F \subseteq E$ by restricting the scalar multiplication. This paper studies the structure of these underlying Lie algebra in relation to the structure of…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
We define a family of graphs we call dual systolic graphs. This definition comes from graphs that are duals of systolic simplicial complexes. Our main result is a sharp (up to constants) isoperimetric inequality for dual systolic graphs.…
We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real…
There are some results on nilpotent Lie algebras $ L $ investigate the structure of $ L $ rely on the study of its $2$-nilpotent multiplier. It is showed that the dimension of the $2$-nilpotent multiplier of $ L $ is equal to $ \frac{1}{3}…
We show that if $G$ is a simple triangle-free graph with $n\geq 3$ vertices, without a perfect matching, and having a minimum degree at least $\frac{n-1}{2}$, then $G$ is isomorphic either to $C_5$ or to $K_{\frac{n-1}{2},\frac{n+1}{2}}$.
We geometrically describe the relation induced on a set of graphs by isomorphism of their associated graph C*-algebras as the smallest equivalence relation generated by five types of moves. The graphs studied have finitely many vertices and…
In this paper, we introduce the notion of a dual topological graph of a given topological graph, and show that it defines a C*-algebra isomorphic to the C*-algebra of the given one. Repeating to take a dual, and taking a projective limit,…
We classify nilpotent associative algebras of dimensions up to 4 over any field. This is done by constructing the nilpotent associative algebras as central extensions of algebras of smaller dimension, analogous to methods known for…
Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different…
A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n+1. In our previous work with Baez and Hoffnung, we described how the `higher analogs' of the…
We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. This also yields the classification of the rigid nilpotent…