Graded contractions of bilinear invariant forms of Lie algebras

We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found. The results can be applied to all Lie algebras and superalgebras (finite or infinite dimensional) which admit the chosen gradings. We consider some examples: contractions of the Killing form, toroidal contractions of $su(3)$, and we briefly discuss the limit to new WZW actions.Comment: 15 page

Graded Contractions of Affine Kac-Moody Algebras

The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and representations. After the introduction of the horizontal and vertical gradings, and the algorithm to find the horizontal toroidal gradings, I discuss some general properties of the graded contractions, and compare them with the In\"on\"u-Wigner contractions. The example of $\hat A_2$ is discussed in detail.Comment: 23 pages, Ams-Te

Family centered nursing practices towards women and their families in the birthing context: A qualitative systematic review

Aim Synthesize qualitative evidence examining how nurses' attitudes, beliefs, and sense of efficacy and the context surrounding birth facilitate or hinder family-centered nursing practice. Design Thematic synthesis of qualitative studies. Methods A literature search was conducted in CINAHL, MEDLINE, PsycINFO, SCOPUS, SCIENCE DIRECT, REPÈRES, CAIRN, and ÉRUDIT from October 2020 to June 2021. The PRISMA guidelines were followed, and studies were critically appraised using the Critical Appraisal Skills Programme checklist. Data were extracted by two independent reviewers, and Thomas and Harden's qualitative thematic synthesis method was performed for data analysis. Results Thirteen studies were included. Three analytical themes were generated: (1) sharing power: opposing beliefs, (2) feeling a sense of efficacy in fulfilling one's role, and (3) managing a challenging work environment. Patient or Public Contribution Synthesizing nurses' experience is essential to promote implementation of favourable changes for care that is more focused on the needs of families

Central extensions of the families of quasi-unitary Lie algebras

The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.Comment: 23 pages. Latex2e fil

The family of quaternionic quasi-unitary Lie algebras and their central extensions

The family of quaternionic quasi-unitary (or quaternionic unitary Cayley--Klein algebras) is described in a unified setting. This family includes the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well as many non-semisimple real Lie algebras which can be obtained from these simple algebras by particular contractions. The algebras in this family are realized here in relation with the groups of isometries of quaternionic hermitian spaces of constant holomorphic curvature. This common framework allows to perform the study of many properties for all these Lie algebras simultaneously. In this paper the central extensions for all quasi-simple Lie algebras of the quaternionic unitary Cayley--Klein family are completely determined in arbitrary dimension. It is shown that the second cohomology group is trivial for any Lie algebra of this family no matter of its dimension.Comment: 17 pages, LaTe

Casimir invariants for the complete family of quasi-simple orthogonal algebras

A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given.Comment: 19 pages, LaTe

Production of Pairs of Sleptoquarks in Hadron Colliders

We calculate the cross section for the production of pairs of scalar leptoquarks (sleptoquarks) in a supersymmetric $E_6$ model, at hadron colliders. We estimate higher order corrections by including $\pi^2$ terms induced by soft-gluon corrections. Discovery bounds on the sleptoquark mass are estimated at collider energies of 1.8, 2, and 4 TeV (Tevatron), and 16 TeV (LHC).Comment: 8 pages, REVTEX, (1 fig. available on request), LAVAL-PHY-94-13/McGILL-94-26/SPhT-94-07