Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter

We discover the unique, simple Lie Algebra of the Third Kind, or LATKe, that stems from codimension 6 orbifold singularities and gives rise to a kind of Yang-Mills theory which simultaneously is pure and contains matter. The root space of the LATKe is 1-dimensional and its Dynkin diagram consists of one point. The uniqueness of the LATKe is a vacuum selection mechanism.Comment: 42 pages; version appearing in JM

Topics on n-ary algebras

We describe the basic properties of two n-ary algebras, the Generalized Lie Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology relevant for the central extensions and infinitesimal deformations of FAs. It is seen that semisimple FAs do not admit central extensions and, moreover, that they are rigid. This extends the familiar Whitehead's lemma to all $n\geq 2$ FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is no longer required to be fully skewsymmetric one is led to the n-Leibniz (or Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz algebras, those with an anticommutative n-bracket, we study the class of n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first n-1 entires of the n-Leibniz bracket.Comment: 11 page

Cohomology of Filippov algebras and an analogue of Whitehead's lemma

We show that two cohomological properties of semisimple Lie algebras also hold for Filippov (n-Lie) algebras, namely, that semisimple n-Lie algebras do not admit non-trivial central extensions and that they are rigid i.e., cannot be deformed in Gerstenhaber sense. This result is the analogue of Whitehead's Lemma for Filippov algebras. A few comments about the n-Leibniz algebras case are made at the end.Comment: plain latex, no figures, 29 page

Classification of simple linearly compact n-Lie superalgebras

We classify simple linearly compact n-Lie superalgebras with n>2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras of the form L=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g, where dim L_{n-1}=1, L_{-1} and L_{n-1} generate L, and [L_j, L_{n-j-1}] =0 for all j, thereby reducing it to the known classification of simple linearly compact Lie superalgebras and their Z-gradings. The list consists of four examples, one of them being the n+1-dimensional vector product n-Lie algebra, and the remaining three infinite-dimensional n-Lie algebras.Comment: Final version to appear in Communications in Mathematical Physic

Cartan-Weyl 3-algebras and the BLG Theory I: Classification of Cartan-Weyl 3-algebras

As Lie algebras of compact connected Lie groups, semisimple Lie algebras have wide applications in the description of continuous symmetries of physical systems. Mathematically, semisimple Lie algebra admits a Cartan-Weyl basis of generators which consists of a Cartan subalgebra of mutually commuting generators H_I and a number of step generators E^\alpha that are characterized by a root space of non-degenerate one-forms \alpha. This simple decomposition in terms of the root space allows for a complete classification of semisimple Lie algebras. In this paper, we introduce the analogous concept of a Cartan-Weyl Lie 3-algebra. We analyze their structure and obtain a complete classification of them. Many known examples of metric Lie 3-algebras (e.g. the Lorentzian 3-algebras) are special cases of the Cartan-Weyl 3-algebras. Due to their elegant and simple structure, we speculate that Cartan-Weyl 3-algebras may be useful for describing some kinds of generalized symmetries. As an application, we consider their use in the Bagger-Lambert-Gustavsson (BLG) theory.Comment: LaTeX. 34 pages.v2. deleted some distracting paragraphs in the introduction to bring more out the main results of the paper. typos corrected and references adde

The Biosynthesis of Artemisinin (Qinghaosu) and the Phytochemistry of Artemisia annua L. (Qinghao)

The Chinese medicinal plant Artemisia annua L. (Qinghao) is the only known source of the sesquiterpene artemisinin (Qinghaosu), which is used in the treatment of malaria. Artemisinin is a highly oxygenated sesquiterpene, containing a unique 1,2,4-trioxane ring structure, which is responsible for the antimalarial activity of this natural product. The phytochemistry of A. annua is dominated by both sesquiterpenoids and flavonoids, as is the case for many other plants in the Asteraceae family. However, A. annua is distinguished from the other members of the family both by the very large number of natural products which have been characterised to date (almost six hundred in total, including around fifty amorphane and cadinane sesquiterpenes), and by the highly oxygenated nature of many of the terpenoidal secondary metabolites. In addition, this species also contains an unusually large number of terpene allylic hydroperoxides and endoperoxides. This observation forms the basis of a proposal that the biogenesis of many of the highly oxygenated terpene metabolites from A. annua - including artemisinin itself may proceed by spontaneous oxidation reactions of terpene precursors, which involve these highly reactive allyllic hydroperoxides as intermediates. Although several studies of the biosynthesis of artemisinin have been reported in the literature from the 1980s and early 1990s, the collective results from these studies were rather confusing because they implied that an unfeasibly large number of different sesquiterpenes could all function as direct precursors to artemisinin (and some of the experiments also appeared to contradict one another). As a result, the complete biosynthetic pathway to artemisinin could not be stated conclusively at the time. Fortunately, studies which have been published in the last decade are now providing a clearer picture of the biosynthetic pathways in A. annua. By synthesising some of the sesquiterpene natural products which have been proposed as biogenetic precursors to artemisinin in such a way that they incorporate a stable isotopic label, and then feeding these precursors to intact A. annua plants, it has now been possible to demonstrate that dihydroartemisinic acid is a late-stage precursor to artemisinin and that the closely related secondary metabolite, artemisinic acid, is not (this approach differs from all the previous studies, which used radio-isotopically labelled precursors that were fed to a plant homogenate or a cell-free preparation). Quite remarkably, feeding experiments with labeled dihydroartemisinic acid and artemisinic acid have resulted in incorporation of label into roughly half of all the amorphane and cadinane sesquiterpenes which were already known from phytochemical studies of A. annua. These findings strongly support the hypothesis that many of the highly oxygenated sesquiterpenoids from this species arise by oxidation reactions involving allylic hydroperoxides, which seem to be such a defining feature of the chemistry of A. annua. In the particular case of artemisinin, these in vivo results are also supported by in vitro studies, demonstrating explicitly that the biosynthesis of artemisinin proceeds via the tertiary allylic hydroperoxide, which is derived from oxidation of dihydroartemisinic acid. There is some evidence that the autoxidation of dihydroartemisinic acid to this tertiary allylic hydroperoxide is a non-enzymatic process within the plant, requiring only the presence of light; and, furthermore, that the series of spontaneous rearrangement reactions which then convert thi allylic hydroperoxide to the 1,2,4-trioxane ring of artemisinin are also non-enzymatic in nature

Experimental investigation of the deepening of the combustion front into peat layers different in botanical composition

The deepening of the center of combustion into peat layers of different botanical compositions (pine-cotton grass and grass-sphagnum peats), typical for the Tomsk region, was investigated experimentally. Peats were ignited from a model ground forest fire initiated by firing of a needle-litter layer. As a result of laboratory investigations, the change in the temperature in the bulk of peat samples with time was determined and analyzed, and the rates of their combustion in the horizontal and vertical directions were estimated. It was established that a fire penetrates deep into a layer of grass-sphagnum peat, containing more than 70% of combustion conductors in its composition, more rapidly as compared to that of pine-cotton grass peat. The rates of combustion of grass-sphagnum peat in the vertical and horizontal directions are larger by 20 and 22%, respectively, than those of pine-cotton grass peat, which is evidently due to the botanical composition of grass-sphagnum peat and the random arrangement of components in its layers

Experimental investigation of the deepening of the combustion front into peat layers different in botanical composition

The deepening of the center of combustion into peat layers of different botanical compositions (pine-cotton grass and grass-sphagnum peats), typical for the Tomsk region, was investigated experimentally. Peats were ignited from a model ground forest fire initiated by firing of a needle-litter layer. As a result of laboratory investigations, the change in the temperature in the bulk of peat samples with time was determined and analyzed, and the rates of their combustion in the horizontal and vertical directions were estimated. It was established that a fire penetrates deep into a layer of grass-sphagnum peat, containing more than 70% of combustion conductors in its composition, more rapidly as compared to that of pine-cotton grass peat. The rates of combustion of grass-sphagnum peat in the vertical and horizontal directions are larger by 20 and 22%, respectively, than those of pine-cotton grass peat, which is evidently due to the botanical composition of grass-sphagnum peat and the random arrangement of components in its layers