Related papers: On the Lie algebra structure of integrable derivat…

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

This article studies the algebraic structure of homology theories defined by a left Hopf algebroid U over a possibly noncommutative base algebra A, such as for example Hochschild, Lie algebroid (in particular Lie algebra and Poisson), or…

We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of $2d$ integrable models. These Lie algebras are defined by the set of infinitesimal, nonlinear, and…

Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. The second main…

We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

Let $p$ be a nonzero complex number. Recently, a class of infinite rank Lie conformal algebras $\mathfrak{B}(p)$ was introduced in [13]. In this paper, we study the structure theory of this class of Lie conformal algebras. Specifically, we…

We provide general closed-form formulas for the index of type-A Lie poset algebras corresponding to posets of restricted height. Furthermore, we provide a combinatorial recipe for constructing all posets corresponding to type-A Frobenius…

We study the problem of the existence of filtered multiplicative bases of a restricted enveloping algebra u(L), where L is a finite-dimensional and p-nilpotent restricted Lie algebra over a field of positive characteristic p.

Let $L$ be one of the finite dimensional Lie algebras $W_n({\bf m}),$ $S_n({\bf m}),$ $ H_n({\bf m})$ of Cartan type over an algebraically closed field of prime characteristic $p>0.$ For an elements $F$ of the symmetrical algebra $S(L)$ we…

We present a formalization, in the theorem prover Lean, of the classification of solvable Lie algebras of dimension at most three over arbitrary fields. Lie algebras are algebraic objects which encode infinitesimal symmetries, and as such…

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 study symplectic structures on filiform Lie algebras -- nilpotent Lie algebras of the maximal length of the descending central sequence. In the present article we classify the Lie algebras with the structure relations of the following…

We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein…

Let $P$ be an arbitrary partially ordered set, $R$ a commutative ring with identity and $FI(P,R)$ the finitary incidence algebra of $P$ over $R$. Under some natural assumption on $R$, we prove that each Lie-type derivation of $FI(P,R)$ is…

We give explicit formulas proving restrictedness of the following Lie (super)algebras: known exceptional simple vectorial Lie (super)algebras in characteristic 3, deformed Lie (super)algebras with indecomposable Cartan matrix, and (under…

Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the…

For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring D(L) constructed by Lichtman. If U(L) is an Ore domain, D(L) coincides with its ring of fractions. It is well known that the…

We show that the p-operator in the Witt algebra (the restricted Lie algebra of derivations of the quotient of the polynomial algebra over a field of characteristic p by the ideal generated by the p-th power of the indeterminant) is given by…

We give an interpretation of the Brauer group of a purely inseparable extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted Lie-Rinehart…