In this talk I will report the recent progress in construction of gauge theories defined on non-commutative (NC) spaces with non-constant non-commutativity parameter $\Theta(x)$. Working in the framework of L-infinity algebras we specify the undeformed gauge theory through the initial set of brackets. Then we introduce the non-commutative deformation as an additional bracket and solve the homotopy relations to complete the bigger L-infinity algebra which describes the corresponding NC gauge theory. In doing so we obtain the expressions for the non-commutative (non-associative) deformation of the U(1) gauge symmetry and the corresponding gauge covariant derivative. The commutator relation for the covariant derivatives defines the NC field strength. The NC deformation of Bianchi identity is defined. We construct the gauge invariant action and obtain the NC field equations which are gauge covariant and reproduce the Maxwell equations in the commutative limit. We work out several explicit examples of non-commutative and non-associative deformations, like the kappa-Minkowski space, su(2)-like Lie-Poisson structure and the constant R-flux.
ID riunione: 858 0971 8040