In this paper, we show that via a novel construction every rank-3 root system induces a root system of rank 4. Via the Cartan-Dieudonné theorem, an even number of successive Coxeter reflections yields rotations that in a Clifford algebra framework are described by spinors. In three dimensions these spinors themselves have a natural four-dimensional Euclidean structure, and discrete spinor group...

Linum spp. (Linaceae) has been shown to accumulate cytotoxic lignans such as podophyllotoxin and 6-methoxypodopyllotoxin. Therefore, plant cell and tissue cultures of Linum spp. may be possible alternative sources for the lignan production. In this study, we focused on the production of lignans by root cultures of Linum spp. Hairy root cultures of L. nodiflorum, L.album and L. austriacum and ro...

introduction: an important consideration in endodontic treatment is the elimination of microorganisms, including fungi, from the complex three- dimensional root canal system. candida albicans (ca) has a major role in endodontic treatment failure as the most important fungus isolated from the root canal system. the present study was carried out to evaluate the presence of ca in the teeth requiri...

We use fermionic representations to obtain a class of BC N -graded Lie algebras coordinatized by quantum tori with nontrivial central extensions. 0 Introduction Lie algebras graded by the reduced finite root systems were first introduced by Berman-Moody [BM] in order to understand the generalized intersection matrix algebras of Slodowy. [BM] classified Lie algebras graded by the root systems of...