Related papers: F-manifold color algebras
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
In this paper we explore a new method of analysis of associative algebras.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
Some new algebraic structures related to the coloured Yang-Baxter equation, and termed coloured Hopf algebras, are reviewed. Coloured quantum universal enveloping algebras of Lie algebras are defined in this context. An extension to the…
We introduce moduli spaces of colored graphs, defined as spaces of non-degenerate metrics on certain families of edge-colored graphs. Apart from fixing the rank and number of legs these families are determined by various conditions on the…
The Jacobian algebras are introduced and their various properties are studied.
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
We define F-algebra--Rinehart pairs and super F-algebroids and study the connection between them.
In this paper we introduce mixed coloured permutation, permutations with certain coloured cycles, and study the enumerative properties of these combinatorial objects. We derive the generating function, closed forms, recursions and…
Quite recently, a ``coloured'' extension of the Yang-Baxter equation has appeared in the literature and various solutions of it have been proposed. In the present contribution, we introduce a generalization of Hopf algebras, to be referred…
This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.
The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and…
Holomorphic manifolds over Cayley-Dickson algebras are defined and their embeddings and immersions are studied.
The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie…
In this paper, we introduce the concept of complementary edge ideals of graphs and study their algebraic properties and invariants.
This paper investigates the geometric and algebraic interplay between F-manifolds and a newly defined class of structures termed F$_\text{man}$-algebras. We specialize our study to the category of F-Lie groups, characterized by a Lie group…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.