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- L. Frappat, P. Sorba, A. Sciarrino
- 1996

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)

- P. Sorba
- 2002

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)

- P. Sorba
- 2003

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)

- L. Frappat, A. Sciarrino, P. Sorba
- 1998

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)

- M. Mintchev, P. Sorba
- 2002

We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not only on their difference. We show that a specific extension of a boundary algebra encodes the underlying scattering… (More)

- M. Mintchev, P. Sorba
- 2004

We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dimensions, to the study of finite temperature quantum field theory with impurities in higher dimensions. We consider a scalar field in (s + 1) + 1 space-time dimensions , interacting with impurities localized on… (More)

- B. Bellazzini, M. Mintchev, P. Sorba
- 2008

We investigate the impact of boundary bound states on the dynamics of quantum fields, which propagate on star graphs modeling quantum wires. These states are localized in the vertex of the graph and decay exponentially in the bulk. We demonstrate that their contribution is completely fixed by causality (local commutativity), which represents a key point of… (More)

- L. Frappat, A. Sciarrino, P. Sorba
- 2003

It has been argued that the sum of usage probabilities for codons, belonging to quartets, that have as third nucleotide C or A, is independent of the biological species for vertebrates. The comparison between the theoretical correlation matrix derived from these sum rules and the experimentally computed matrix for 26 species shows a satisfactory agreement.… (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)

- P. Sorba
- 1992

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)