Related papers: Monopole star products are non-alternative
We explicitly construct an L$_\infty$ algebra that defines U$_{\star}(1)$ gauge transformations on a space with an arbitrary non-commutative and even non-associative star product. Matter fields are naturally incorporated in this scheme as…
The theory of unified product and extending structures for alternative and pre-alternative algebras are developed. It is proved that the extending structures of these algebras can be classified by using some non-abelian cohomology and…
Motivated by M-theory, we define a new type of non-associative algebra involving usual and cubic matrices at the same time. The resulting algebra can be regarded as a two-term truncated $L_\infty$ algebra giving rise to a fundamental…
A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…
We present a deformed star-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators…
A non-Hermitian coupled waveguide system with periodically varying parameters, in which the Berry curvature is analogous to a hyperbolic magnetic monopole or antimonopole, is investigated. It is shown to have a purely imaginary Berry…
It is shown that non-commutative spaces, which are quotients of associative algebras by ideals generated by non-linear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of…
We analyze the nonrelativistic quantum scattering problem of a charged particle by an Abelian magnetic monopole in the background of a global monopole. In addition to the magnetic and geometric effects, we consider the influence of the…
Theory of pointlike magnetic monopole with an arbitrary magnetic charge is considered. It is shown that a proper description requires making use of nonunitary representations of the rotation group and the nonassociative generalization of…
A new non-associative algebra for the quantization of strongly interacting fields is proposed. The full set of quantum $(\pm)$associators for the product of three operators is offered. An algorithm for the calculation of some…
In this paper we extend the analysis of magnetic monopoles in quantum mechanics in three dimensional rotationally invariant noncommutative space $\textbf{R}^3_\lambda$. We construct the model step-by-step and observe that physical objects…
The main non-associative algebras are Lie algebras and Jordan algebras. There are several ways to unify these non-associative algebras and associative algebras.
For a class of nonassociative metagroup algebras their separability is investigated. For this purpose the cohomology theory on them is utilized. Conditions are found under which nonassociative metagroup algebras are separable. Algebras…
Contrary to the classical methods of quantum mechanics, the deformation quantization can be carried out on phase spaces which are not even topological manifolds. In particular, the Moyal star product gives rise to a canonical functor $F$…
In this paper, we review the progress in the analysis of magnetic monopoles as generalized states in quantum mechanics. We show that the considered model contains rich algebraic structure that generates symmetries which have been utilized…
A nonassociative generalization of supersymmetry is studied, where supersymmetry generators are considered to be the nonassociative ones. Associators for the product of three and four multipliers are defined. Using a special choice of the…
We review two known in the literature exemples of non-associative star products. The first one is the phase space star product representing quantization of non-geometric $R$-flux background in closed string theory. The second is the…
Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
It is known that there are Lie algebras with non-semigroup gradings, i.e. such that the binary operation on the grading set is not associative. We provide a similar example in the class of associative algebras.