Related papers: The Freiheitssatz and automorphisms for free brace…
We generalize several recognizability theorems for free single-sorted algebras to the field of many-sorted algebras and provide, in a uniform way and without using neither regular tree grammars nor tree automata, purely algebraic proofs of…
Two varieties $V, W$ of the same type are independent if there is a binary term $t(x,y)$ such that $V \models t(x,y) \approx x$ and $W \models t(x,y) \approx y$. In this note, we give necessary and sufficient conditions for two finite…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
We study an analogue of the Andreadakis-Johnson filtration for automorphism groups of free algebras and introduce the notion of tangent Lie algebras for certain automorphism groups, defined as subalgebras of the Lie algebra of derivations.…
An algebra is said to be a unary Leibniz algebra if every one-generated subalgebra is a Leibniz algebra. An algebra is said to be a binary Leibniz algebra if every two-generated subalgebra is a Leibniz algebra. We give characterizations of…
Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best…
It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…
We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable…
Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear…
Based on Bergman's Lemma on centralizers, we obtain a sharp lower degree bound for nonconstant elements in a subalgebra generated by two elements of a free associative algebra over an arbitrary field.
We investigate the action of Schur algebra on the Lie algebras of derivations of free Lie algebras and operad structures constructed from it. We also show that the Lie algebra of derivations is generated by quadratic derivations together…
We provide an internal characterization of those finite algebras (i.e., algebraic structures) $\mathbf A$ such that the number of homomorphisms from any finite algebra $\mathbf X$ to $\mathbf A$ is bounded from above by a polynomial in the…
We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a…
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
Any variety of classical algebras has a so-called conformal counterpart. For example one can consider Lie conformal or associative conformal algebras. Lie conformal algebras are closely related to vertex algebras. We define free objects in…
We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization,…
We provide a construction of free factorization algebras in algebraic geometry and link factorization homology of a scheme with coefficients in a free factorization algebra to the homology of its (unordered) configuration spaces. As an…
A base of a relatively free associative algebra with the identity x^3=0 over a field of arbitrary characteristic is found. As an application a minimal generating system of the 3x3 matrix invariant algebra is determined.
Let $k$ be a complete non-archimedean non-trivial valued field. In this paper, we investigate whether every $k$-algebra homomorphism between $k$-affinoid algebras is automatically bounded. We show that this property holds if and only if…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…