Related papers: Making Non-Associative Algebra Associative
An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a(bc)+(ab)c=0. Such algebras are nilpotent. We describe the free anti-associative algebras with a finite number of generators. Other types…
We investigate the noncommutative gauge theories arising on the worldvolumes of D-branes in non-geometric backgrounds obtained by T-duality from twisted tori. We revisit the low-energy effective description of D-branes on three-dimensional…
Over the past quarter century, considerable effort has been invested in the study of nonrelativistic (NR) string theory, its U-dual NR brane theories, and their geometric foundations in (generalized) Newton-Cartan geometry. Many interesting…
We show that geometric theories with $p$-form gauge fields have a nonassociative symmetry structure, extending an underlying Lie algebra. This nonassociativity is controlled by the same Chevalley-Eilenberg cohomology that classifies free…
We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' models proposed in string theory. We use the theory of quasialgebras obtained by cochain twist introduced previously. The gauge theory…
In this short paper the noncommutative geometry and quantization of branes and the AdS is discussed. The question in part addresses an open problem left by this author in [1] on how branes are generated by stringy physics. The breaking of…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.
We propose a new class of non-factorising D-branes in the product group GxG where the fluxes and metrics on the two factors do not necessarily coincide. They generalise the maximally symmetric permutation branes which are known to exist…
We introduce the new notion of epsilon-graded associative algebras which takes its root into the notion of commutation factors introduced in the context of Lie algebras. We define and study the associated notion of epsilon-derivation-based…
We review some recent results on the extension of the gauge/gravity correspondence to include matter in the fundamental representation by adding D-branes to the supergravity backgrounds. Working in the quenched approximation, in which the…
We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation…
In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the…
New extended superspaces associated with topological charge algebras of the D-brane are used to construct D-brane actions without worldvolume gauge fields. The actions are shown to be kappa-symmetric under an appropriately chosen right…
In this thesis we discuss non-perturbative phenomena emerging in gauge and in string/supergravity theories. We compute the partition function of 5D minimal supersymmetric U(1) gauge theory with extra adjoint matter in general…
The principal observation of the present paper is that an inner isotopy (i.e. a principal isotopy defined by an algebra endomorphism) is a very helpful instrument in constructing and studying interesting classes of nonassociative algebras.…
Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L$_\infty$ algebra, that governs not only the action of the symmetries but also…