Related papers: Geometric Classification of 4-Dimensional Superalg…

The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore…

We briefly overview the Petrov classification in four dimensions and its generalization to higher dimensions.

We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.

{\small In this paper, we find a class of division quaternion algebras over the field }$\mathbb{Q}\left( i\right) ${\small \ and a class of division symbol algebras over a cyclotomic field.}

We give an introduction to the study of algebraic hypersurfaces, focusing on the problem of when two hypersurfaces are isomorphic or close to being isomorphic. Working with hypersurfaces and emphasizing examples makes it possible to discuss…

We address the problem of when two finite dimensional central division algebras over the same field are necessarily isomorphic given that they have the same maximal subfields.

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…

A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

In the present paper we present a classification of Lie bialgebra structures on Lie algebras of type g[[u]] and g[u], where g is a simple finite dimensional Lie algebra.

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.

Geometric vertex algebras are a simplified version of Huang's geometric vertex operator algebras. We give a self-contained account of the equivalence of geometric vertex algebras with Z-graded vertex algebras.

In this paper, we give an expansion of two notions of double extension and $T^*$-extension for quadratic and odd quadratic Lie superalgebras. Also, we provide a classification of quadratic and odd quadratic Lie superalgebras up to dimension…

This paper is devoted to the complete algebraic and geometric classification of complex $5$-dimensional nilpotent binary Leibniz and $4$-dimensional nilpotent mono Leibniz algebras. As a corollary, we have the complete algebraic and…

Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically…

A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…

We give a geometric classification of $n$-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent algebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit…

We develop new techniques to classify basic algebras of blocks of finite groups over algebraically closed fields of prime characteristic. We apply these techniques to simplify and extend previous classifications by Linckelmann, Murphy and…

We classify, up to isomorphism, the 2-dimensional algebras over a field K. We focuse also on the case of characteristic 2, identifying the matrices of GL(2,F_2) with the elements of the symmetric group S_3. The classification is then given…

The paper presents a classification of quadratic extension algebras, also known as algebras of degree 2, as well as several characterizations of quaternion algebras over a field (of characteristic not 2). The presentation is not restricted…