Related papers: Algebraic Isomorphism of Limit Algebras

We classify isomorphism types of unital commutative algebras of rank 7 over an algebraically closed field of characteristic not 2 or 3 completely.

It is shown that the fixed point subalgebra of an EALA under a finite order automorphism (satisfying certain properties) is a sum of EALA's, an abelian subalgebra, and a subspace which is contained in the centralizer of the core.

The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…

Let $\Omega$ denote an algebra of sets and $\mu$ a $\sigma$-finite measure. We then prove that the completion of $\Omega$ under the pseudometric $d(A,B)$ = $\mu^{\ast}(A \triangle B)$ is $\sigma$-algebra isomorphic and isometric to the…

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…

The isomorphism problem for infinite finitely presented groups is probably the hardest among standard algorithmic problems in group theory. Classes of groups where it has been completely solved are nilpotent groups, hyperbolic groups, and…

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

An algebraic deformation theory of coalgebra morphisms is constructed.

In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which…

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…

In this paper, we introduce the concepts of representation and dual representation for averaging Leibniz algebras. We also develop a cohomology theory for these algebras. Additionally, we explore the infinitesimal and formal deformation…

We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…

We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

We prove that a certain homological epimorphism between two algebras induces a triangle equivalence between their singularity categories. Applying the result to a construction of matrix algebras, we describe the singularity categories of…

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…

We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation.…

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…