Related papers: Infinite dimensional primitive linearly compact Li…
We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of…
In this paper, we characterize the super-biderivations of Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that all super-biderivations of Cartan type simple Lie superalgebras are inner…
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of…
We classify, up to equivalence, all finite-dimensional simple graded division algebras over the field of real numbers. The grading group is any finite abelian group.
This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
The set of points of a one-dimensional cut-and-project quasicrystal or model set, while not additive, is shown to be multiplicative for appropriate choices of acceptance windows. This leads to the definition of an associative additive…
We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…
We prove Conjecture 5.7 in [arXiv:1409.2532], describing all inclusions between primitive ideals for the general linear superalgebra in terms of the Ext1-quiver of simple highest weight modules. For arbitrary basic classical Lie…
It is shown that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by 2 elements.
We classify closed abelian subgroups of the automorphism group of any compact classical simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup, and describe Weyl groups of maximal abelian subgroups.
The paper is devoted to give a full classification of all finite dimensional nilpotent Lie algebras $ L $ of class $4$ such that $ \dim L^2=3. $ Moreover, we classify the capable ones.
It is shown that if the universal enveloping algebra of a simple $\mathbb Z^n$-graded Lie algebra is Noetherian, then the Lie algebra is finite-dimensional.
We determine normal forms of the multiplication of four-dimensional anti-commutative algebras over a field $\mathbb K$ of characteristic zero having an analogous family of flags of subalgebras as the four-dimensional non-Lie binary Lie…
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…
Results describing Lie ideals and maximal finite-codimensional Lie subalgebras of the Lie algebras associated with Lie algebroids with non-singular anchor maps are presented. It is also proved that every isomorphism of such Lie algebras…
We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple Z-graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain…
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras $L=\sum_{i\in \mathbb Z}L_i,$ over an algebraically closed field of characteristic…