A pre-Lie product is a binary operation whose associator is symmetric in the last two variables. As a consequence its antisymmetrization is a Lie bracket. In this paper we study the symmetrization of the pre-Lie product. We show that it does not satisfy any other universal relation than commutativity. This means that the map from the free commutative-magmatic algebra to the free pre-Lie algebra...

Ceramic brackets have gained widespread acceptance in orthodontic treatment due to their superior aesthetic appeal. The immediate popularity of these brackets, after their initial marketing, was tempered by their potential to damage the enamel during debonding. This paper describes the design and development of a ceramic bracket that addresses the failings of most ceramic brackets on the market...

In this paper we discuss some aspects of the frame formulation of conformal higher spins in three dimensions. We give some exact formulae for the coupled spin twospin three part of the full higher spin theory and propose a star product Lagrangian for all spins from two and up. Since there is no consistent Lagrangian formulation based on the Poisson bracket we start the construction from the fie...

The superconformal algebras of Ademollo et al are generalised to a multi-index form. The structure obtained is similar to the Moyal Bracket analogue of the Neveu-Schwarz Algebra.

The deformation theory of an algebra is controlled by the Gerstenhaber bracket, a Lie bracket on Hochschild cohomology. We develop techniques for evaluating brackets semidirect product algebras recording actions finite groups over fields positive characteristic. cohomology and these skew group can be complicated when characteristic underlying field divides order. show how to investigate using t...

We prove that non-coisotropic branes in the Poisson-Sigma model are allowed at the quantum level. When the brane is defined by second-class constraints, the perturbative quantization of the model yields Kontsevich’s star product associated to the Dirac bracket on the brane. Finally, we present the quantization for a general brane.

We introduce the notion of bipolar fuzzy Lie sub-superalgebras (resp. bipolar fuzzy ideals) and present some of their properties. First we investigate the properties of bipolar fuzzy Lie sub-superalgebras and bipolar fuzzy ideals under homomorphisms of Lie superalgebras. Next we study bipolar fuzzy bracket product, solvable bipolar fuzzy ideals and nilpotent bipolar fuzzy ideals of Lie superalg...

background and aims. the aim of this study was to compare shear bond strength (sbs) of metal and ceramic brackets bonded to enamel using acid versus er:yag laser etching. materials and methods. eighty premolars were divided into 4 groups: am (acid etching/ metal brackets), ac (acid etching/ ceramic brackets), lm (laser etching/ metal brackets) and lc (laser etching/ ceramic brackets). enamel co...

We will extend the classical derived bracket construction to any algebra over a binary quadratic operad. We will show that the derived product construction is a functor given by the Manin white product with the operad of permutation algebras. As an application, we will show that the operad of prePoisson algebras is isomorphic to Manin black product of the Poisson operad with the preLie operad. ...