Related papers: Multi-parameter formal deformations of ternary hom…
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of…
We define three fundamental solvable bilinear deformations for any massive non-relativistic 2d quantum field theory (QFT). They include the $\mathrm{T}\overline{\mathrm{T}}$ deformation and the recently introduced hard rod deformation. We…
On Hom-Lie algebras and superalgebras,we introduce the notions of biderivations, linear commuting maps and {\alpha}-biderivations, and compute them for some typical Hom-Lie algebras and superalgebras, including q-deformed W(2,2) algebra,…
The aim of this paper is to provide a cohomology of $n$-Hom-Lie color algebras governing one parameter formal deformations. Then, we study formal deformations of a $n$-Hom-Lie color algebra and introduce the notion of Nijenhuis operator on…
We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical…
Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these…
(Multiplicative) Hom-Lie-Yamaguti superalgebras which generalize Hom-Lie supertriple systems (and subsequently ternary multiplicative Hom-Nambu superalgebras) and Hom-Lie superalgebras in the same way as Lie-Yamaguti superalgebras [Frac]…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
This paper begins by introducing the concept of a quasi-hom-Lie algebra which is a natural generalization of hom-Lie algebras introduced in a previous paper by the authors. Quasi-hom-Lie algebras include also as special cases (color) Lie…
We construct a three-parameter deformation of the Hopf algebra $\LDIAG$. This is the algebra that appears in an expansion in terms of Feynman-like diagrams of the {\em product formula} in a simplified version of Quantum Field Theory. This…
We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed…
We investigate formal deformations of certain classes of nonassociative algebras including classes of K[{\Sigma}3]-associative algebras, Lie-admissible algebras and anti-associative algebras. In a process which is similar to Poisson algebra…
By considering $p,q$-deformed and $\mu$-deformed algebras we propose an association of them to form a hybrid deformed algebra. The increased number of available parameters can provide us with a richer tool to investigate new scenarios…
A ternary Nambu-Poisson algebra (which we call a Nambu-Poisson algebra in the paper) is the underlying algebraic structure of Nambu-Poisson manifolds of order $3$ that appeared in the generalized Hamiltonian mechanics. First, we consider…
In this work we introduce a novel q-deformation of the Virasoro algebra expressed in terms of free fermions, we then realize that this algebra, when the deformation parameter is a root of unity can be realized exactly on the lattice. We…
This work is devoted to the algebraic and arithmetic properties of Rankin-Cohen brackets allowing to define and study them in several natural situations of number theory. It focuses on the property of these brackets to be formal…
Hom-Bol algebras are defined as a twisted generalization of (left) Bol algebras. Hom-Bol algebras generalize multiplicative Hom-Lie triple systems in the same way as Bol algebras generalize Lie triple systems. The notion of an $n$th derived…