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.
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)
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)
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)
This paper analyses the Noether symmetries and the corresponding conservation laws for Chern-Simons Lagrangians in dimension d = 3. In particular, we find an expression for the superpotential of Chern-Simons gravity. As a by-product the general discussion of superpoten-tials for 3rd order natural and quasi-natural theories is also given.
A new notion of an optimum first order calculi was introduced in [Borowiec, Kharchenko and Oziewicz, 1993]. A module of vector fields for a coordinate differential is defined. Some examples of optimal algebras for homogeneous bimodule commutations are presented. Classification theorem for homogeneous calculi with commutative optimal algebras in two… (More)
A new family of Nyquist pulses for coherent optical single carrier systems is introduced and is shown to increase the nonlinearity tolerance of dual-polarization (DP)-QPSK and DP-16-QAM systems. Numerical investigations for a single-channel 28 Gbaud DP-16-QAM long-haul system without optical dispersion compensation indicate that the proposed pulse can… (More)
A new notion of Cartan pairs as a substitute of notion of vector fields in the noncommutative geometry is proposed. The correspondence between Cartan pairs and differential calculi is established.