13 research outputs found
The classification of almost affine (hyperbolic) Lie superalgebras
We say that an indecomposable Cartan matrix A with entries in the ground
field of characteristic 0 is almost affine if the Lie sub(super)algebra
determined by it is not finite dimensional or affine but the Lie (super)algebra
determined by any submatrix of A, obtained by striking out any row and any
column intersecting on the main diagonal, is the sum of finite dimensional or
affine Lie (super)algebras. A Lie (super)algebra with Cartan matrix is said to
be almost affine if it is not finite dimensional or affine, and all of its
Cartan matrices are almost affine.
We list all almost affine Lie superalgebras over complex numbers correcting
two earlier claims of classification and make available the list of almost
affine Lie algebras obtained by Li Wang Lai.Comment: 92 page
Cytoplasmic diversity of Brassica napus L., Brassica oleracea L. and Brassica rapa L. as determined by chloroplast microsatellite markers
Genetic validity of RAPD markers at the intra- and inter-specific level in wild Brassica species with n=9
Survey and genetic diversity of wild Brassica oleracea L. germplasm on the Atlantic coast of France
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Simple sequence repeats reveal uneven distribution of genetic diversity in chloroplast genomes of Brassica oleracea L. and (n=9) wild relatives
Diversity in the chloroplast genome of 171 accessions representing the Brassica 'C' (n = 9) genome, including domesticated and wild B. oleracea and nine inter-fertile related wild species, was investigated using six chloroplast SSR (microsatellite) markers. The lack of diversity detected among 105 cultivated and wild accessions of B. oleracea contrasted starkly with that found within its wild relatives. The vast majority of B. oleracea accessions shared a single haplotype, whereas as many as six haplotypes were detected in two wild species, B. villosa Biv. and B. cretica Lam.. The SSRs proved to be highly polymorphic across haplotypes, with calculated genetic diversity values (H) of 0.23-0.87. In total, 23 different haplotypes were detected in C genome species, with an additional five haplotypes detected in B. rapa L. (A genome n = 10) and another in B. nigra L. (B genome, n = 8). The low chloroplast diversity of B. oleracea is not suggestive of multiple domestication events. The predominant B. oleracea haplotype was also common in B. incana Ten. and present in low frequencies in B. villosa, B. macrocarpa Guss, B. rupestris Raf. and B. cretica. The chloroplast SSRs reveal a wealth of diversity within wild Brassica species that will facilitate further evolutionary and phylogeographic studies of this important crop genus