Related papers: Geometric Classification of 4-Dimensional Superalg…
A complete classification of two-dimensional algebras over algebraically closed fields is provided
We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.
We classify up to equivalence the gradings on Hurwitz superalgebras and on symmetric composition superalgebras, over any field. Also, classifications up to isomorphism are given in case the field is algebraically closed. By grading, here we…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
The algebraic and geometric classifications of complex $3$-dimensional right alternative superalgebras are given. As a byproduct, we have the algebraic and geometric classification of the variety of $3$-dimensional $\mathfrak{perm}$, binary…
This paper is devoted to give the complete algebraic and geometric classification of $4$-dimensional nilpotent Novikov algebras over $\mathbb C.$
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
A study is made of real Lie algebras admitting a hypersymplectic structure, and we provide a method to construct such hypersymplectic Lie algebras. We use this method in order to obtain the classification of all hypersymplectic structures…
A superfield formalism for quantum fields with N-extended superconformal symmetry is developed using vertex algebra techniques in four dimensions.
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
We classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and…
We classify the $4$-dimensional nilpotent bicommutative algebras over $\mathbb C$ from both algebraic and geometric approaches.