It has been recently shown that, in the first order (Palatini) formalism , there is universality of Einstein equations and Komar energy– momentum complex, in the sense that for a generic nonlinear La-grangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the… (More)
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative geometry and particle systems with generalized statistics are indicated.
Two one-parameter families of twists providing κ−Minkowski * −product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. First one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. An other one relies on an… (More)
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in . In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial differential operators as well as its natural (Fock type) representation. We shall also define co-universal vector fields and… (More)
We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Nöther currents and superpotentials are computed so that results are easily compared with the well-known results in dimension 3. Finally we use this covariant formulation… (More)
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl–Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates… (More)
General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal differential calculus on these structures is then defined and its basic properties investigated.
It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (sym-metrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-Hermitian metric on a complex manifold… (More)
Chern–Simons type Lagrangians in d = 3 dimensions are analyzed from the point of view of their covariance and globality. We use the transgression formula to find out a new fully covariant and global Lagrangian for Chern–Simons gravity: the price for establishing globality is hidden in a bimetric (or biconnection) structure. Such a formulation allows to… (More)
The theory of ternary semigroups, groups and algebras is reformulated in the abstract arrow language. Then using the reversing arrow ansatz we define ternary comultiplication, bialgebras and Hopf algebras and investigate their properties. The main property " to be binary derived " is considered in detail. The co-analog of Post theorem is formulated. It is… (More)