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A deformed q-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the 1 algebra of a q-deformed boson. The limit of this algebra when q is a n-th root of unity is also studied in detail. By means of(More)
Newly introduced generalized Poisson structures based on suitable skew–sym-metric contravariant tensors of even order are discussed in terms of the Schouten-Nijenhuis bracket. The associated 'Jacobi identities' are expressed as conditions on these tensors, the cohomological contents of which is given. In particular, we determine the linear generalized(More)
The super or Z 2-graded Schouten-Nijenhuis bracket is introduced. Using it, new generalized super-Poisson structures are found which are given in terms of certain graded-skew-symmetric contravariant tensors Λ of even order. The corresponding super 'Jacobi identities' are expressed by stating that these tensors have zero super Schouten-Nijenhuis bracket with(More)
New generalized Poisson structures are introduced by using skew-symmetric contravariant tensors of even order. The corresponding 'Jacobi identities' are given by the vanishing of the Schouten-Nijenhuis bracket. As an example, we provide the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras. 1 Standard(More)
BACKGROUND/AIMS Podocytes are critical in maintaining the filtration barrier of the glomerulus and are dependent on the slit diaphragm. We hypothesized that disturbances of podocyte biology contribute to proteinuria in women with preeclampsia (PE). METHODS A human podocyte cell line was stimulated with serum from women with PE (patients) and healthy(More)
New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding 'Jacobi iden-tities' are provided by conditions on these tensors, which may be understood as cocycle conditions. As an example, we provide the linear generalized Poisson structures which can be constructed on the dual(More)
We show that one-dimensional superspace is isomorphic to a non-trivial but consistent limit as q → −1 of the braided line. Supersymmetry is identified as translational invariance along this line. The supertranslation generator and covariant derivative are obtained in the limit in question as the left and right derivatives of the calculus on the braided line.