Related papers: Model completeness and quantifier elimination for …

In this paper we show that evolution algebras over any given field $\Bbbk$ are universally finite. In other words, given any finite group $G$, there exist infinitely many regular evolution algebras $X$ such that $Aut(X)\cong G$. The proof…

We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in…

Building over recent results, we expand the basic theory of algebraic extensions to the realm of superfields -a field with multivalued sum and product-, showing that every superfield has a (unique up to isomorphism) strong algebraic…

Faithful representations of regular $\ast$-rings and modular complemented lattices with involution within orthosymmetric sesquilinear spaces are studied within the framework of Universal Algebra. In particular, the correspondence between…

In this thesis we discuss some properties of centralisers in classical Lie algebas and related structures. Our results follow three distinct but related themes: the modular representation theory of centralisers, the sheets of simple Lie…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

We show that the first order structure whose underlying universe is $\mathbb C$ and whose basic relations are all algebraic subset of $\mathbb C^2$ does not have quantifier elimination. Since an algebraic subset of $\mathbb C ^2$ needs…

Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we…

The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

This paper describes the centers of the universal enveloping algebras and the invariant rings of the standard filiform Lie algebras over fields of characteristic zero and also over large enough prime characteristic. We determine explicit…

In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.

We establish the existence of Springer isomorphisms for reductive group schemes over general base schemes. For this, we first study centralizers of fiberwise regular sections of reductive group schemes, and we establish their flatness in…

The only C*-algebras that admit elimination of quantifiers in continuous logic are $\mathbb{C}, \mathbb{C}^2$, $C($Cantor space$)$ and $M_2(\mathbb{C})$. We also prove that the theory of C*-algebras does not have model companion and show…

We give a necessary and sufficient smoothness condition for the scheme parameterizing the n-dimensional representations of a finitely generated associative algebra over an algebraically closed field of characteristic zero. In particular,…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…

We describe all irreducible conformal subalgebras of Cend_N. The classification of simple and semisimple associative conformal algebras with finite faithful representation follows from this description.

Say that a cone is a commutative monoid in which x+y=0 implies that x=y=0. We show that cones (resp. simple cones) of many kinds order-embed or even embed unitarily into refinement cones (resp. simple refinement cones) of the same kind,…

An alternative, geometrical proof of a known theorem concerning the decomposition of positive maps of the matrix algebra $M_{2}(\mathbb{C})$ has been presented. The premise of the proof is the identification of positive maps with operators…