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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.
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)
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)
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)