Related papers: Parafermionic and Generalized Parafermionic Algebr…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…
This note is an expanded and updated version of our entry with the same title for the 2006 Encyclopedia of Mathematical Physics. We give a brief overview of graded Poisson algebras, their main properties and their main applications, in the…
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to…
We show that deformed Heisenberg algebra with reflection emerging in parabosonic constructions is also related to parafermions. This universality is discussed in different algebraic aspects and is employed for the description of spin-j…
Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$. We will show that those…
Universal algebraic geometry allows considering of geometric properties of every universal algebra. When two algebras have same algebraic geometry? We must consider the categories of algebraic closed sets of these algebras to answer this…
In this paper, we define generalized braid theories in alignment with the language of Fenn and Bartholomew for knot theories, and compute a generating set for the pure generalized braid theories. Using this, we prove that every oriented…
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
Generalized Virasoro algebras (defined as the universal central extension of some generalized Witt algebras) and super-Virasoro algebras and modules of the intermediate series are studied and discussed.
In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebra, a Weyl algebra, an infinite rank matrix algebra, and an affine Kac-Moody algebra. We also…
Decomposition algebras and axial decomposition algebras are classes of commutative nonassociative algebras which are generalizations of axial algebras. The classes decomposition algebras, axial decomposition al;gebras and non-primitive…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and…
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a…
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…