Related papers: Special functions as structure constants for new i…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts. The first is a generalization of the KP equation and contains 9 arbitrary…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of…
In this paper, we study a special class of indefinite Kac-Moody algebras. Based on the study of hyperbolic Kac-Moody algebras, we give the definition of $N_k$ type Kac-Moody algebras and study some properties of this special type Kac-Moody…
We introduce a new class of infinite-dimensional Lie algebras, which we refer to as continuum Kac-Moody algebras. Their construction is closely related to that of usual Kac-Moody algebras, but they feature a continuum root system with no…
We discuss the higher dimensional generalizations of the Virasoro and Affine Kac-Moody Lie algebras. We present an explicit construction for a central extensions of the Lie Algebra $Map (X, \g)$ where $\g$ is a finite-dimensional Lie…
In this paper, using the tools from the lineability theory, we distinguish certain subsets of $p$-adic differentiable functions. Specifically, we show that the following sets of functions are large enough to contain an infinite dimensional…
We present the structural constants of low dimensional pseudo $H$-type algebras.
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
In this paper, we analyze multi-dimensional Weyl almost periodic type functions in Lebesgue spaces with variable exponents. The introduced classes seem to be new and not considered elsewhere even in the constant coefficient case. We provide…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
We use non-perturbative U-duality symmetries of type II strings to construct new vacuum solutions. In some ways this generalizes the F-theory vacuum constructions. We find the possibilities of new vacuum constructions are very limited.…
Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of…
A lot of developments made during the last years show that Kac-Moody algebras play an important role in the algebraic structure of some supergravity theories. These algebras would generate infinite-dimensional symmetry groups. The possible…
Some integral properties of Jack polynomials, hypergeometric functions and invariant polynomials are studied for real normed division algebras.
Nongraded infinite-dimensional Lie algebras appeared naturally in the theory of Hamiltonian operators, the theory of vertex algebras and their multi-variable analogues. They play important roles in mathematical physics. This survey article…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…