Related papers: On absolute nilpotent and idempotent elements of a…

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.

We obtain the complete Lie point symmetry algebras of two sequences of odd-order evolution equations. This includes equations that are fully-nonlinear, i.e. nonlinear in the highest derivative. Two of the equations in the sequences have…

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 give a direct construction of a specific idempotent in the endomorphism algebra of a finite lattice $T$. This idempotent is associated with all possible sublattices of $T$ which are total orders.

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is…

We study almost inner derivations of $2$-step nilpotent Lie algebras of genus $2$, i.e., having a $2$-dimensional commutator ideal, using matrix pencils. In particular we determine all almost inner derivations of such algebras in terms of…

We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…

We are interested in the evolution operators defined on commutative and nonassociative algebras when the scalar field is of characteristic 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic and plenary train…

We show that a complex structure on a nilpotent almost abelian real Lie algebra is unique if it exists. As a consequence, we get full control over the cohomology and deformations of almost abelian complex nilmanifolds.

We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserving expansions.

Nilpotent Leibniz algebras with isomorphic maximal subalgebras are considered. The algebras are classified for coclass zero, one, and two. The results are field dependent.

Let \theta be an involution of the semisimple Lie algebra g and g=k+p be the associated Cartan decomposition. The nilpotent commuting variety of (g,\theta) consists in pairs of nilpotent elements (x,y) of p such that [x,y]=0. It is…

In this paper we give classification of two-dimensional real evolution algebras. For several chains of evolution algebras we study their classification dynamics.

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.

We give algebraic and geometric classifications of $6$-dimensional complex nilpotent anticommutative algebras. Specifically, we find that, up to isomorphism, there are $14$ one-parameter families of $6$-dimensional nilpotent anticommutative…

Ideas from deformation quantization are applied to deform the expression of elements of an algebra. Extending these ideas to certain transcendental elements implies that $\frac{1}{i\h}uv$ in the Weyl algebra is naturally viewed as an…

Consider a bisexual population such that the set of females can be partitioned into finitely many different types indexed by $\{1,2,\dots,n\}$ and, similarly, that the male types are indexed by $\{1,2,\dots,\nu \}$. Recently an evolution…

This paper is devoted to the complete algebraic classification of complex $5$-dimensional nilpotent Novikov algebras.

We formulate the notion of continuous evolution algebra in terms of differentiable matrix-valued functions, to then study those such algebras arising as solutions of ODE problems. Given their dependence on natural bases, matrix Lie groups…

We develop a general theory of $W$-algebras in the context of supersymmetric vertex algebras. We describe the structure of $W$-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As…