We review the present status of gauge theories built on various quantum space–times
described by noncommutative space–times. The mathematical tools and notions underlying …

We give a pedagogical account of noncommutative gauge and gravity theories, where the
exterior product between forms is deformed into a⋆-product via an abelian twist (eg the …

We define a new homotopy algebraic structure, that we call a braided L_ ∞ L∞-algebra,
and use it to systematically construct a new class of noncommutative field theories, that we …

We study the differential and Riemannian geometry of algebras $ A $ endowed with an
action of a triangular Hopf algebra $ H $ and noncomutativity compatible with the associated …

We propose a sheaf-theoretic approach to the theory of differential calculi on quantum
principal bundles over non-affine bases. After recalling the affine case we define differential …

We study covariant derivatives on a class of centered bimodules ℰ over an algebra 𝒜. We
begin by identifying a 𝒵 (𝒜)-submodule 𝒳 (𝒜) which can be viewed as the analogue of …

We prove the existence and uniqueness of Levi-Civita connections for strongly σ-compatible
pseudo-Riemannian metrics on tame differential calculi. Such pseudo-Riemannian metrics …

Arbitrary connections on a generic Hopf algebra H are studied and shown to extend to
connections on tensor fields. On this ground a general definition of metric compatible …

We propose a general procedure to construct noncommutative deformations of an
embedded submanifold M of R n determined by a set of smooth equations fa (x)= 0. We use …

We propose a general procedure to construct noncommutative deformations of an algebraic
submanifold M of ℝ n R^n, specializing the procedure G. Fiore, T. Weber, Twisted …