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Foreword The main definitions and properties of Lie superalgebras are proposedà la façon 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(More)
We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q → 1 each subalgebra specializes to the enveloping algebra U(k), where k is a fixed point subalgebra of the loop algebra gl N [λ, λ −1 ] with respect to a natural involution corresponding to the embedding(More)
Inspired by factorized scattering from delta–type impurities in (1+1)-dimensional space-time, we propose and analyse a generalization of the Zamolodchikov–Faddeev algebra. Distinguished elements of the new algebra, called reflection and transmission generators, encode the particle–impurity interactions. We describe in detail the underlying algebraic(More)
The quantum enveloping algebra U q (sl(2) ⊕ sl(2)) in the limit q → 0 is proposed as a symmetry algebra for the genetic code. In this approach the triplets of nucleotids or codons in the DNA chain are classified in crystal bases, tensor product of U q→0 (sl(2) ⊕ sl(2)) representations. Such a construction might be compared to the baryon classification from(More)
New developments are presented in the framework of the model introduced bythe authors in References [1, 2] and in which nucleotides as well ascodons are classified in crystal bases of the quantum group U(q)(sl(2) ⊕ sl (2)) in the limit q → 0. An operator whichgives the correspondence between the amino-acids and the codons isobtained for any known genetic(More)
We present a classification of W algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an Sl(2) subalgebra (resp. OSp(1|2) superalgebra) of a simple Lie algebra (resp. superalgebra) G. However, the determination of an U(1) Y factor, commuting with Sl(2) (resp.(More)