相关论文: Word equations in simple groups and polynomial equ…
We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the $\psi$-sum. We also provide similar descriptions…
Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl…
A study of harmonic maps into Lie groups as a generalisation of the study of other well-known integrable systems, particularly the Toda and self-dual Chern Simons theories.
In this paper, we define and study (co)homology theories of a compatible associative algebra $A$. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define…
We develop layered monoidal theories -- a generalisation of monoidal theories combining formal descriptions of a system at different levels of abstraction. Via their representation as string diagrams, monoidal theories provide a graphical…
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…
The relationship between algebraic geometry and the inferential framework of the Bayesian Networks with hidden variables has now been fruitfully explored and exploited by a number of authors. More recently the algebraic formulation of…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We exhibit explicit orthogonal decompositions of every multidimensional restricted root space of a real semi-simple Lie algebra. We then show a link between this result and a radiality property of smooth functions on G-homogeneous spaces…
We study the interrelation of space functions of groups and the space complexity of the algorithmic word problem in groups.
In this paper we explore a new method of analysis of associative algebras.
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
In response to questions by Kassabov, Nikolov and Shalev, we show that a given subset $A$ of a finite simple group $G$ is the image of some word map $w : G\times G\to G $ if and only if (i) $A$ contains the identity and (ii) $A$ is…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
The aim of the paper is to extend the class of generalized Weyl algebras to a larger class of rings (they are also called {\em generalized Weyl algebras}) that are determined by two ring endomorphisms rather than one as in the case of `old'…
The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…