Related papers: The moduli space of 4-dimensional non-nilpotent co…

In this paper, we study 4-dimensional nilpotent complex associative algebras. This is a continuation of the study of the moduli space of 4-dimensional algebras. The non-nilpotent algeras were analyzed in an earlier paper. Even though there…

In this paper, we study the moduli space of $2|1$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $1|2$-dimensional complex space. We construct the moduli space by…

In this paper, we study the moduli space of $1|2$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $2|1$-dimensional complex space. We construct the moduli space by…

In this paper, we give a classification of the 3-dimensional associative algebras over the complex numbers, including a construction of the moduli space, using versal deformations to determine how the space is glued together.

In this paper, we study moduli spaces of low dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of…

In this paper, we study moduli spaces of 2-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.

We study the moduli space of four dimensional ordinary Lie algebras, and their versal deformations. Their classification is well known; our focus in this paper is on the deformations, which yield a picture of how the moduli space is…

In this paper, we study the moduli space of $1|1$-dimensional complex associative algebras. We give a complete calculation of the cohomology of every element in the moduli space, as well as compute their versal deformations.

In this paper, we study the moduli space of all complex 5-dimensional Lie algebras, realizing it as a stratification by orbifolds, which are connected by jump deformations. The orbifolds are given by the action of finite groups on very…

We determine the moduli space of metric 2-step nilpotent Lie algebras of dimension up to 6. This space is homeomorphic to a cone over a 4-dimensional contractible simplicial complex.

This paper is a contribution to the development of the non associative algebras theory. More precisely, this work deals with the classification of the complex 4-dimensional Leibniz algebras. Note that the classification of 4-dimensional…

In this paper, we consider the versal deformations of three dimensional Lie algebras. We classify Lie algebras and study their deformations by using linear algebra techniques to study the cohomology. We will focus on how the deformations…

In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of nxn matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give…

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…

Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…

We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb C$ from both algebraic and geometric approaches.