Related papers: A complete classification of three-dimensional alg…
The graded Lie algebra associated with the Nottingham group over a field of prime characteristic serves as a fundamental example of Nottingham algebras, a class of infinite-dimensional, positively graded thin algebras. This paper completes…
We classify, up to isomorphism and up to equivalence, involutions on graded-division finite-dimensional simple real (associative) algebras, when the grading group is abelian.
The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the current paper, we present a study of nilpotent triassociative…
We give a comprehensive survey of the theory of finite dimensional Lie algebras over an algebraically closed field of characteristic p>0 and announce that for p>3 the classification of finite dimensional simple Lie algebras is complete. Any…
We give a geometric classification of 4-dimensional superalgebras over an algebraic closed field.
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimension less than four, as…
We introduce the notion of Lie algebras with plus-minus pairs as well as regular plus-minus pairs. These notions deal with certain factorizations in universal enveloping algebras. We show that many important Lie algebras have such pairs and…
We present a complete list of 6-dimensional Manin triples or, equivalently, of 3-dimensional Lie bialgebras. We start from the well known classification of 3-dimensional real Lie algebras and assume the canonical bilinear form on the…
Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained:…
In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model. We also extrapolate the ideas for the cyclic 3-leg triangular…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
We study gradings by abelian groups on associative algebras with involution over an arbitrary field. Of particular importance are the fine gradings (that is, those that do not admit a proper refinement), because any grading on a…
This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for…
In this paper we describe central extensions (up to isomorphism) of all complex null-filiform and filiform associative algebras.
The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.
We initiate the study of computable presentations of real and complex C*-algebras under the program of effective metric structure theory. With the group situation as a model, we develop corresponding notions of recursive presentations and…
It is not commonly realized that the algebra of complex numbers can be used in an elegant way to represent the images of ordinary 3-dimensional figures, orthographically projected to the plane. We describe these ideas here, both using…
In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex…
We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…