510 research outputs found
Dictionary on Lie Superalgebras
The main definitions and properties of Lie superalgebras are proposed a la
facon de a short dictionary, the different items following the alphabetical
order. The main topics deal with the structure of simple Lie superalgebras and
their finite dimensional representations; rather naturally, a few pages are
devoted to supersymmetry. This modest booklet has two ambitious goals: to be
elementary and easy to use. The beginner is supposed to find out here the main
concepts on superalgebras, while a more experimented theorist should recognize
the necessary tools and informations for a specific use.Comment: 145p LaTeX Document, also available at
http://lapphp0.in2p3.fr/preplapp/psth/DICTIONARY_SUPER.ps.g
Crystalizing the genetic code
New developments are presented in the framework of the model introduced by
the authors in refs. [1,2] and in which nucleotides as well as codons are
classified in crystal bases of the quantum group U_q(sl(2)+sl(2)) in the limit
q -> 0. An operator which gives the correspondence between the amino-acids and
the codons is now obtained for any known genetic code. The free energy released
by base pairing of dinucleotides as well as the relative hydrophilicity and
hydrophobicity of the dinucleosides are also computed. For the vertebrate
series, a universal behaviour in the ratios of codon usage frequencies is put
in evidence and is shown to fit nicely in our model. Then a first attempt to
represent the mutations relative to the deletion of a pyrimidine by action of a
suitable crystal spinor operator is proposed. Finally recent theoretical
descriptions are reviewed and compared with our model
A minimum principle in mRNA editing ?
mRNA editing of sequences of many species is analyzed. The nature of the
inserted nucleotides and the position of the insertion sites, once fixed the
edited peptide chain, are explained by introducing a minimum principle in the
framework of the crystal basis model of the genetic code introduced by the
authors.Comment: revised extended version - includes analysis on more dat
From quantum to elliptic algebras
It is shown that the elliptic algebra at the
critical level c=-2 has a multidimensional center containing some trace-like
operators t(z). A family of Poisson structures indexed by a non-negative
integer and containing the q-deformed Virasoro algebra is constructed on this
center. We show also that t(z) close an exchange algebra when p^m=q^{c+2} for m
integer, they commute when in addition p=q^{2k} for k integer non-zero, and
they belong to the center of when k is odd. The
Poisson structures obtained for t(z) in these classical limits contain the
q-deformed Virasoro algebra, characterizing the structures at generic values of
p, q and m as new algebras.Comment: LaTeX2e Document - packages subeqn,amsfont
Anyonic Realization of the Quantum Affine Lie Algebras
We give a realization of the quantum affine Lie algebras \uqa and \uqc in
terms of anyons defined on a one-dimensional chain (or on a two-dimensional
lattice), the deformation parameter being related to the statistical
parameter of the anyons by . In the limit of the
deformation parameter going to one we recover the Feingold-Frenkel fermionic
construction of undeformed affine Lie algebras.Comment: 8p, LaTeX, subeqn.sty. Also available at
http://lapphp0.in2p3.fr/preplapp/psth/anyon_ac.ps.g
Central extensions of classical and quantum q-Viraroso algebras
We investigate the central extensions of the q-deformed (classical and
quantum) Virasoro algebras constructed from the elliptic quantum algebra
A_{q,p}[sl(N)_c]. After establishing the expressions of the cocycle conditions,
we solve them, both in the classical and in the quantum case (for sl(2)). We
find that the consistent central extensions are much more general that those
found previously in the literature.Comment: Latex2e, needs amsfonts and amssymb package
Deformed W_N algebras from elliptic sl(N) algebras
We extend to the sl(N) case the results that we previously obtained on the
construction of W_{q,p} algebras from the elliptic algebra
A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the
critical level c=-N has an extended center containing trace-like operators
t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining
q-deformations of the W_N algebra, are constructed. The operators t(z) also
close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes
Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson
structures obtained in these classical limits contain different q-deformed W_N
algebras depending on the parity of h, characterizing the exchange structures
at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page
Symmetry and Codon Usage Correlations in the Genetic Code
The ratios of the codon usage in the quartets and sextets for the vertebrate
series exhibit a correlated behaviour which fits naturally in the framework of
the crystal basis model of the genetic code. Moreover the observed universal
behaviour of these suitably normalized ratios can be easily explained.Comment: 6 figures, documen
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