Efim Zelmanov
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Jordan homomorphisms and T-ideals Open
Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $φ:A\to B$ is the sum of a homomorphism…
Cuspidal modules over Superconformal algebras of rank \geq 1 Open
According to V. Kac and J. van de Leur, the superconformal algebras are the simple $\Z$-graded Lie superalgebras of growth one which contains the Witt algebra. We describe an explicit classification of all cuspidal modules over the known s…
Simple Jordan superalgebras with the even parts of Clifford type Open
The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts a…
On Lie isomorphisms of rings Open
An associative ring $A$ gives rise to the Lie ring $A^{(-)}=(A,[a,b ]=ab-ba)$. The subject of isomorphisms of Lie rings $A^{(-)}$ and $[A,A]$ has attracted considerable attention in the literature. We prove that if the identity element of …
Cyclic homology of Jordan superalgebras and related Lie superalgebras Open
We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras. …
View article: On the complexity of subshifts and infinite words
On the complexity of subshifts and infinite words Open
We characterize the complexity functions of subshifts up to asymptotic equivalence. The complexity function of every aperiodic function is non-decreasing, submultiplicative and grows at least linearly. We prove that conversely, every funct…
Mathematical Proof Between Generations Open
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Automorphisms and derivations of affine commutative and PI-algebras Open
We prove analogs of A.~Selberg's result for finitely generated subgroups of $\text{Aut}(A)$ and of Engel's theorem for subalgebras of $\text{Der}(A)$ for a finitely generated associative commutative algebra $A$ over an associative commutat…
Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth Open
We construct finitely generated nil algebras with prescribed growth rate. In particular, any increasing submultiplicative function is realized as the growth function of a nil algebra up to a polynomial error term and an arbitrarily slow di…
Mathematical Proof Between Generations Open
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Topological Lie bialgebra structures and their classification over $ \mathfrak{g}[\![x]\!] $ Open
This paper is devoted to a classification of topological Lie bialgebra structures on the Lie algebra $\mathfrak{g}[\![x]\!]$, where $ \mathfrak{g} $ is a finite-dimensional simple Lie algebra over an algebraically closed field $ F $ of cha…
The restricted Burnside problem for Moufang loops Open
We prove that for positive integers $m \geq 1, n \geq 1$ and a prime number $p \neq 2,3$ there are finitely many finite m -generated Moufang loops of exponent $p^n$ .
Finite presentability of universal central extensions of ${\mathfrak{sl}_n}$ Open
In this paper we discuss finite presentability of the universal central extensions of Lie algebras ${\mathfrak{sl}_n(R)}$, where $n\geq 3$ and $R$ is a unital associative $k$-algebra. We show that a universal central extension is finitely …
On the Morita equivalence class of a finitely presented algebra Open
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
On Pro-$2$ Identities of $2\times2$ Linear Groups Open
Let $\hat{F}$ be a free pro-$p$ non-abelian group, and let $Δ$ be a commutative Noetherian complete local ring with a maximal ideal $I$ such that $\textrm{char}(Δ/I)=p>0$. In [Zu], Zubkov showed that when $p\neq2$, the pro-$p$ congruence s…
Matrix wreath products of algebras and embedding theorems Open
We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §6, we construct finitely …
A finite presentation of Jordan algebras Open
Let [Formula: see text] be an associative algebra. Let [Formula: see text] be an involution. We study the following question: when are the Jordan algebras [Formula: see text] and [Formula: see text] finitely presented?
On matrix wreath products of algebras Open
We introduce a new construction of matrix wreath products of algebras that is similar to the construction of wreath products of groups introduced by L. Kaloujnine and M. Krasner [17]. We then illustrate its usefulness by proving embedding …
Lie algebras and torsion groups with identity Open
We prove that a finitely generated Lie algebra L such that (i) every commutator in generators is ad-nilpotent, and (ii) L satisfies a polynomial identity, is nilpotent. As a corollary we get that a finitely generated residually- p torsion …
Algebras and semigroups of locally subexponential growth Open
We prove that a countable dimensional associative algebra (resp. a countable semigroup) of locally subexponential growth is $M_\infty$-embeddable as a left ideal in a finitely generated algebra (resp. semigroup) of subexponential growth. M…
Matrix wreath products of algebras and embedding theorems Open
We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In §\ref{Section6}, we constr…
On Lie rings of torsion groups Open
We prove that the Lie ring associated to the lower central series of a finitely generated residually-p torsion group is graded nil.
Local nilpotency of the McCrimmon radical of a Jordan system Open
Using the fact that absolute zero divisors in Jordan pairs become Lie sandwiches of the corresponding Tits–Kantor–Koecher Lie algebras, we prove local nilpotency of the McCrimmon radical of a Jordan system (algebra, triple system, or pair)…