Related papers: Finite Relation Algebras
Let $\mathfrak{g}$ be a real finite-dimensional Lie algebra equipped with a symmetric bilinear form $\langle\cdot,\cdot\rangle$. We assume that $\langle\cdot,\cdot\rangle $ is nil-invariant. This means that every nilpotent operator in the…
A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…
It is well known that the subvariety lattice of the variety of relation algebras has exactly three atoms. The (join-irreducible) covers of two of these atoms are known, but a complete classification of the (join-irreducible) covers of the…
We show that the symmetrization of a brace algebra structure yields the structure of a symmetric brace algebra.
We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities…
We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…
We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with the number of nodes. Furthermore, we show that when the…
The connections between Tarski's relation algebras and Thompson's groups F, T, V, and his monoid M are reviewed here, along with Jonsson-Tarski algebras, fork algebras, true pairing algebras, and tabular relation algebras. All of these…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
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…
Two structures $M, N$ in the same language are called probably isomorphic if they (or, in case of metric structures, their completions) are isomorphic after forcing with the Lebesgue measure algebra. We show that, if $M$ and $N$ are…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \in A$. We prove that…
We determine the solvable complete Lie algebras whose nilradical is isomorphic to a filiform Lie algebra. Moreover we show that for any positive integer $n$ there exists a solvable complete Lie algebras whose second cohomology group with…
We provide the analytic expressions of the totally symmetric and anti-symmetric structure constants in the $\mathfrak{su}(N)$ Lie algebra. The derivation is based on a relation linking the index of a generator to the indexes of its non-null…
This paper investigates the homology of the Brauer algebras, interpreted as appropriate Tor-groups, and shows that it is closely related to the homology of the symmetric group. Our main results show that when the defining parameter of the…
Let $\alpha\geq 2$ be any ordinal. We consider the class $\mathsf{Drs}_{\alpha}$ of relativized diagonal free set algebras of dimension $\alpha$. With same technique, we prove several important results concerning this class. Among these…
Relativization is one of the central topics in the study of algebras of relations. Some relativized relation algebras behave much nicer than the original relation algebras. In this paper, we study the atomicity of the finitely generated…
We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…
We show that in a prime nonassociative Novikov algebra every nonzero ideal is non-associative. We prove that Baer (and Andrunakievich) radical and left quasiregular radical coincide in finite dimensional Novikov algebras over a field of…