On the embedding of universal algebras in groupoids holding the law $XY\ast ZU\ast \ast = XZ\ast YU\ast \ast $

M. D. Radojčić

Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law $X Y * Z U * * = X Z * Y U * *$ ”

Antiassociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2017)

Mathematica Bohemica

Similarity:

Given a groupoid $〈 G, ☆ 〉$ , and $k \geq 3$ , we say that $G$ is antiassociative if an only if for all $x_{1}, x_{2}, x_{3} \in G$ , $(x_{1} ☆ x_{2}) ☆ x_{3}$ and $x_{1} ☆ (x_{2} ☆ x_{3})$ are never equal. Generalizing this, $〈 G, ☆ 〉$ is $k$ -antiassociative if and only if for all $x_{1}, x_{2}, ..., x_{k} \in G$ , any two distinct expressions made by putting parentheses in $x_{1} ☆ x_{2} ☆ x_{3} ☆ \dots ☆ x_{k}$ are never equal. We prove that for every $k \geq 3$ , there exist finite groupoids that are $k$ -antiassociative. We then generalize this, investigating when other pairs of groupoid terms can be made never equal.

The infinitesimal counterpart of tangent presymplectic groupoids of higher order

P. M. Kouotchop Wamba, A. MBA (2018)

Archivum Mathematicum

Similarity:

Let $(G, ω)$ be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, $(T^{r} G, ω^{(c)})$ where $T^{r} G$ is the tangent groupoid of higher order and $ω^{(c)}$ is the complete lift of higher order of presymplectic form $ω$ .

On cardinalities of algebras of formulas for $ω_{0}$ -categorical theories

Jan Waszkiewicz (1973)

Colloquium Mathematicae

Similarity:

On generalized Beurling’s theorem and symmetry of $L_{1}$ -group algebras

Zenobia Anusiak (1971)

Colloquium Mathematicae

Similarity:

Universal lifting theorem and quasi-Poisson groupoids

David Inglesias-Ponte, Camille Laurent-Gengoux, Ping Xu (2012)

Journal of the European Mathematical Society

Similarity:

We prove the universal lifting theorem: for an $α$ -simply connected and $α$ -connected Lie groupoid $Γ$ with Lie algebroid $A$ , the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative multi-vector fields on $Γ$ . As a consequence, we obtain the integration theorem for a quasi-Lie bialgebroid, which generalizes various integration theorems in the literature in special cases. The second goal of the paper is the study of basic properties of quasi-Poisson groupoids....

Algebraic Superconnections, $S U (2 ∣ 1)$ and Electroweak Interactions

R. Coquereaux (1992)

Recherche Coopérative sur Programme n°25

Similarity:

The structures of Hopf $*$ -algebra on Radford algebras

Hassan Suleman Esmael Mohammed, Hui-Xiang Chen (2019)

Czechoslovak Mathematical Journal

Similarity:

We investigate the structures of Hopf $*$ -algebra on the Radford algebras over $ℂ$ . All the $*$ -structures on $H$ are explicitly given. Moreover, these Hopf $*$ -algebra structures are classified up to equivalence.

Universal embeddings of $l^{1} (α)$ into the space of continuous functions on a product space

N. Kalamidas, Th. Zachariades (1989)

Colloquium Mathematicae

Similarity:

Transfer of derived equivalences from subalgebras to endomorphism algebras II

Shengyong Pan, Jiahui Yu (2024)

Czechoslovak Mathematical Journal

Similarity:

We investigate derived equivalences between subalgebras of some $Φ$ -Auslander-Yoneda algebras from a class of $n$ -angles in weakly $n$ -angulated categories. The derived equivalences are obtained by transferring subalgebras induced by $n$ -angles to endomorphism algebras induced by approximation sequences. Then we extend our constructions in T. Brüstle, S. Y. Pan (2016) to $n$ -angle cases. Finally, we give an explicit example to illustrate our result.

Quantised ${𝔰𝔩}_{2}$ -differential algebras

Andrey Krutov, Pavle Pandžić (2024)

Archivum Mathematicum

Similarity:

We propose a definition of a quantised ${𝔰𝔩}_{2}$ -differential algebra and show that the quantised exterior algebra (defined by Berenstein and Zwicknagl) and the quantised Clifford algebra (defined by the authors) of ${𝔰𝔩}_{2}$ are natural examples of such algebras.

Singularity categories of skewed-gentle algebras

Xinhong Chen, Ming Lu (2015)

Colloquium Mathematicae

Similarity:

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let $(Q^{s g}, I^{s g})$ and $(Q^{g}, I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $K Q^{s g} / ⟨ I^{s g} ⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $K Q^{g} / ⟨ I^{g} ⟩$ . As a corollary, we find that $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

$ℵ_{0}$ -categoricity of products of 1-unary algebras

Philip Olin (1975)

Colloquium Mathematicae

Similarity:

Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

N. Ch. Wass

Similarity:

This thesis is concerned with the problem of determining a measure of algebraic independence for a particular m-tuple θ₁,..., $θ_{m}$ of complex numbers. Specifically, let K be a number field and let f₁(z),..., $f_{m} (z)$ be elements of K[[z]] algebraically independent over K(z) satisfying equations of the form(*) $f_{j} (z^{b}) = \sum_{i = 1}^{m} f_{i} (z) a_{i j} (z) + b_{j} (z)$ (j = i,...,m)for b ≥ 2, $a_{i j} (z)$ , $b_{j} (z)$ in K(z). Suppose finally that α ∈ K is such that 0 < |α| < 1, the $f_{j} (z$ ) converge at z = α and the $a_{i j} (z)$ , $b_{j} (z)$ are analytic at $z = α, α^{b}, α^{b ²}, . . .$ Then the $θ_{i} = f_{i} (α)$ are algebraically independent...

Matrix representation of finite effect algebras

Grzegorz Bińczak, Joanna Kaleta, Andrzej Zembrzuski (2023)

Kybernetika

Similarity:

In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra $E$ we construct set of matrices $M (E)$ in such a way that effect algebras $E_{1}$ and $E_{2}$ are isomorphic if and only if $M (E_{1}) = M (E_{2})$ . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most $8$ .

On the number of finite algebraic structures

Erhard Aichinger, Peter Mayr, R. McKenzie (2014)

Journal of the European Mathematical Society

Similarity:

We prove that every clone of operations on a finite set $A$ , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting $R$ for some finitary relation $R$ over $A$ . It follows that for a fixed finite set $A$ , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...

Multiplicatively dependent triples of Tribonacci numbers

Carlos Alexis Ruiz Gómez, Florian Luca (2015)

Acta Arithmetica

Similarity:

We consider the Tribonacci sequence $T : = {T_{n}}_{n \geq 0}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_{n + 3} = T_{n + 2} + T_{n + 1} + T_{n}$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.

Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law X Y * Z U * * = X Z * Y U * * ”

Displaying similar documents to “On the embedding of universal algebras in groupoids holding the law $X Y * Z U * * = X Z * Y U * *$ ”