Related papers: Making Non-Associative Algebra Associative
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding…
We consider the gauge algebra of closed string field theory with a focus on diffeomorphisms. This algebra contains off-shell information in two ways. The first way is geometric, through the choice of three-punctured sphere defining the…
We examine the role of non-commutative geometry in D$p$-branes within large R-R field backgrounds. In this context, the background of a significant ($p-1$)-form R-R field can be effectively described using a ($p-1$)-bracket, similar to the…
There is a notion of non-commutative Lie algebra called "Leibniz algebra", which is characterized by the condition: left bracketing is a derivation. The purpose of this article is to introduce and study a new notion of algebra, called…
We present a concise overview of the physical and mathematical structures underpinning the appearence of nonassociative deformations of geometry in non-geometric string theory. Starting from a quick recap of the appearence of noncommutative…
We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology,…
The Newton-Hooke algebras in d dimensions are constructed as contractions of dS(AdS) algebras. Non-relativistic brane actions are WZ terms of these Newton-Hooke algebras. The NH algebras appear also as subalgebras of multi-temporal…
Closed string dynamics in the presence of noncommutative Dp-branes is investigated. In particular, we compute bulk closed string two-point scattering amplitudes; the bulk space-time geometries encoded in the amplitudes are shown to be…
An associative central simple algebra is a form of matrices, because a maximal \'{e}tale subalgebra acts on the algebra faithfully by left and right multiplication. In an attempt to extract and isolate the full potential of this point of…
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…
Let $V$ be a vertex algebra and $g$ an automorphism of $V$ of order $T$. We construct a sequence of associative algebras $\tilde{A}_{g,n}(V )$ for any $n\in(1/T)\mathbb{N}$, which are not depend on the conformal structure of $V$. We show…
In this paper, we develop a geometric approach to study derived tame finite dimensional associative algebras, based on the theory of non-commutative nodal curves.
This paper is devoted to the study of the Hamiltonian dynamics of string in non-relativistic D3-brane background. We discuss different gauge fixing functions and construct corresponding gauge fixed Hamiltonians.
We study new solutions of the low-energy equations of motion for the non-abelian D-string. We find a "fuzzy funnel" solution consisting of a noncommutative four-sphere geometry which expands along the length of the D-string. We show that…
A variety of associative algebras is called nonmatrix if it does not contain the algebra of 2 x 2 matrices over the given field. Nonmatrix varieties were introduced and studied by V.N.Latyshev in relation with the Specht problem. Some…
We study pairs of planar D-branes intersecting on null hypersurfaces, and other related configurations. These are supersymmetric and have finite energy density. They provide open-string analogues of the parabolic orbifold and null-fluxbrane…
We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes' transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical…
The aim of this paper is to establish a contravariant adjunction between the category of quasi-bialgebras and a suitable full subcategory of dual quasi-bialgebras, adapting the notion of finite dual to this framework. Various functorial…
We study nonmatrix varieties of $\mathbf{k}$-algebras, where $\mathbf{k}$ is a unital commutative ring. Our results extend to this generality known results for the case in which $\mathbf{k}$ is an infinite field. Also, we generalize these…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.