How to realize Lie algebras by vector fields

An algorithm for embedding finite dimensional Lie algebras into Lie algebras of vector fields (and Lie superalgebras into Lie superalgebras of vector fields) is offered in a way applicable over ground fields of any characteristic. The algorithm is illustrated by reproducing Cartan's interpretations of the Lie algebra of G(2) as the Lie algebra that preserves certain non-integrable distributions. Similar algorithm and interpretation are applicable to other exceptional simple Lie algebras, as well as to all non-exceptional simple ones and many non-simple ones, and to many Lie superalgebras.Comment: 17 pages, LaTe

A spinor-like representation of the contact superconformal algebra K'(4)

In this work we construct an embedding of a nontrivial central extension of the contact superconformal algebra K'(4) into the Lie superalgebra of pseudodifferential symbols on the supercircle S^{1|2}. Associated with this embedding is a one-parameter family of spinor-like tiny irreducible representations of K'(4) realized just on 4 fields instead of the usual 16.Comment: 19 pages, TeX. Corrections to the references in the paper to be published in J. Math. Phys. v 42, no 1, 200

Minkowski superspaces and superstrings as almost real-complex supermanifolds

In 1996/7, J. Bernstein observed that smooth or analytic supermanifolds that mathematicians study are real or (almost) complex ones, while Minkowski superspaces are completely different objects. They are what we call almost real-complex supermanifolds, i.e., real supermanifolds with a non-integrable distribution, the collection of subspaces of the tangent space, and in every subspace a complex structure is given. An almost complex structure on a real supermanifold can be given by an even or odd operator; it is complex (without "always") if the suitable superization of the Nijenhuis tensor vanishes. On almost real-complex supermanifolds, we define the circumcised analog of the Nijenhuis tensor. We compute it for the Minkowski superspaces and superstrings. The space of values of the circumcised Nijenhuis tensor splits into (indecomposable, generally) components whose irreducible constituents are similar to those of Riemann or Penrose tensors. The Nijenhuis tensor vanishes identically only on superstrings of superdimension 1|1 and, besides, the superstring is endowed with a contact structure. We also prove that all real forms of complex Grassmann algebras are isomorphic although singled out by manifestly different anti-involutions.Comment: Exposition of the same results as in v.1 is more lucid. Reference to related recent work by Witten is adde

Методика идентификации материала стандартного образца состава азитромицина с использованием спектральных методов

In new medicinal products development, as well as actualisation of assessment approaches of medicinal products in circulation, the development of quality control procedures remains one of the most important issues in standardisation. Besides, such development should include using reliable, accurate and sensitive physicochemical methods which determine the need development and implementation of reference materials. This paper discusses the development of reliable methods for identifying the structure of azithromycin, which will guarantee the purity of the reference material, as well as adequately and unambiguously choose a method of quantitative determination in accordance with the current requirements of regulatory acts, and according to the Pharmacopoeia of the Russian Federation of the XIV Edition. При создании новых лекарственных средств, а также актуализации подходов к оценке качества лекарственных средств, находящихся в обращении, важным вопросом стандартизации является разработка методов контроля качества с применением надежных, точных и чувствительных физико-химических методов, что, в свою очередь, обуславливает необходимость создания и использования стандартных образцов. В данной статье рассматривается вопрос о разработке надежных методов идентификации структуры азитромицина, которая позволит гарантировать чистоту стандартного образца, адекватно и однозначно выбрать метод количественного определения в соответствии с действующими требованиями нормативных актов, а также согласно Фармакопее Российской Федерации XIV Издания