Related papers: Left Transitive AG-groupoids
A groupoid satisfying the left invertive law: $ab\cdot c=cb\cdot a$ is called an AG-groupoid and is a generalization of commutative semigroups. We consider the concept of bi-commutativity in AG-groupoids and thus introduce left commutative…
A groupoid that satisfies the left invertive law: $ab\cdot c=cb\cdot a$ is called an AG-groupoid. We extend the concept of left abelian distributive groupoid (LAD) and right abelian distributive groupoid (RAD) to introduce new subclasses of…
A groupoid that satisfying the left invertive law is called an AG-groupoid.this concept is extended to introduce a Stein AG-groupoid. We provethe existence by providing some non-associative examples. We also explore some basic and general…
A groupoid G is called an AG-groupoid if it satisfies the left invertive law: (ab)c = (cb)a. An AG-group G, is an AG-groupoid with left identity e \in G (that is, ea = a for all a \in G) and for all a \in G there exists a' \in G such that…
In this paper, we have investigated different classes of an AG-groupoid by their structural properties. We have prove that weakly regular, intra-regular, right regular, left regular, left quasi regular and completely regular coincide in an…
An AG-monoid is an AG-groupoid (a groupoid satisfying the identity called left invertive law $(xy)z=(zy)x$) and having a left identiy. In this paper we enumerate AG-monoids algebraically and then implement them in GAP to compute them…
A new subclass of AG-groupoids, so called, cyclic associative Abel-Grassman groupoids or CA-AG-groupoid is studied. These have been enumerated up to order $6$. A test for the verification of cyclic associativity for an arbitrary AG-groupoid…
The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…
A completely inverse $AG^{**}$-groupoid is a groupoid satisfying the identities $(xy)z=(zy)x$, $x(yz)=y(xz)$ and $xx^{-1}=x^{-1}x$, where $x^{-1}$ is a unique inverse of $x$, that is, $x=(xx^{-1})x$ and $x^{-1}=(x^{-1}x)x^{-1}$. First we…
A graph $\Ga$ is $G$-symmetric if $\Ga$ admits $G$ as a group of automorphisms acting transitively on the set of vertices and the set of arcs of $\Ga$, where an arc is an ordered pair of adjacent vertices. In the case when $G$ is…
A Lie 2-group $G$ is a category internal to the category of Lie groups. Consequently it is a monoidal category and a Lie groupoid. The Lie groupoid structure on $G$ gives rise to the Lie 2-algebra $\mathbb{X}(G)$ of multiplicative vector…
In this paper we study properties of left (right) division (cancellative) groupoids with associative-like identities, namely, with cyclic associative identity (x (y z) = (z x) y) and Tarki (x (z y) = (x y) z) identities.
We show that a quantum field theory A living on the line and having a group G of inner symmetries gives rise to a category GLoc A of twisted representations. This category is a braided crossed G-category in the sense of Turaev. Its degree…
Given a second-countable, Hausdorff, \'etale, amenable groupoid G with compact unit space, we show that an element a in C*(G) is invertible if and only if \lambda_x(a) is invertible for every x in the unit space of G, where \lambda_x refers…
A subcategory $\textbf{C}$ of a groupoid $\mathbb{G}$ is a left order in $\mathbb{G}$, if every element of $\mathbb{G}$ can be written as $a^{-1}b$ where $a, b \in \textbf{C}$. A subsemigroupoid $\mathfrak{C}$ of a groupoid $\mathbb{G}$ is…
This paper contributes to the characterization of a certain class of commutative Hopf algebroids. It is shown that a commutative flat Hopf algebroid with a non zero base ring and a nonempty character groupoid is geometrically transitive if…
We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G,G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the…
We consider left-invariant $G_2$-structures on $7$-dimensional almost Abelian Lie groups. Also, we characterise the associated torsion forms and the full torsion tensor according to the Lie bracket $A$ of the corresponding Lie algebra. In…
By a completely inverse $AG^{**}$-groupoid we mean an inverse $AG^{**}$-groupoid $A$ satisfying the identity $xx^{-1}=x^{-1}x$, where $x^{-1}$ denotes a unique element of $A$ such that $x=(xx^{-1})x$ and $x^{-1}=(x^{-1}x)x^{-1}.$ We show…
Suppose that $G$ is a groupoid with binary operation $\otimes$. The pair $(G,\otimes)$ is said to be a gyrogroup if the operation $\otimes$ has a left identity, each element $a \in G$ has a left inverse and the gyroassociative law and the…