Related papers: Supernilpotence prevents dualizability

Anticommutative Engel algebras of the first five degeneration levels are classified. All algebras appearing in this classification are nilpotent Malcev algebras.

If G is a non-nilpotent group and nil(G) = {g \in G : <g, h> is nilpotent for all h\in G}, the nilpotent graph of G is the graph with set of vertices G-nil(G) in which two distinct vertices are related if they generate a nilpotent subgroup…

We prove that any Novikov algebra over a field of characteristic $\neq 2$ is Lie-solvable if and only if its commutator ideal $[N,N]$ is right nilpotent. We also construct examples of infinite-dimensional Lie-solvable Novikov algebras $N$…

We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include…

We prove that the cohomology algebra of a conilpotent Lie coalgebra is generated in degree 1 as an A-infinity algebra. By dualizing, the same is true about cohomology algebras of finite dimensional nilpotent Lie algebras. In the process, we…

In this paper, we first introduce the non-abelian cohomology group of a Nijenhuis Lie algebra with values in another Nijenhuis Lie algebra and show that it parametrizes the isomorphism classes of all non-abelian extensions. In particular,…

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants…

In this paper we describe the infinitesimal deformations of null-filiform Leibniz superalgebras over a field of zero characteristic. It is known that up to isomorphism in each dimension there exist two such superalgebras $NF^{n,m}$. One of…

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras…

Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev…

The structure of nilpotent symplectic algebras of maximal class has been studied in [8, 5]. In this paper, we study the dual subclass of algebras of minimal class. In particular, we show that symplectic alternating algebras of dimension up…

An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types…

In this paper, the structure of the second relative homology and the relative stem cover of the direct sum of two pairs of Leibniz algebras are determined by means of the non-abelian tensor product of Leibniz algebras. We also characterize…

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real…

We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras,…

We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur…

In this paper we classify solvable Leibniz algebras whose nilradical is a null-filiform algebra. We extend the obtained classification to the case when the solvable Leibniz algebra is decomposed as a direct sum of its nilradical, which is a…

A nilmanifold is a (left) quotient of a nilpotent Lie group by a cocompact lattice. A hypercomplex structure on a manifold is a triple of complex structure operators satisfying the quaternionic relations. A hypercomplex nilmanifold is a…

The paper concerns nilpotent associative dialgebras and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five-term cohomological sequence under alternative conditions in…