Vertex operators and Jordan fields

The construction of Lie algebras in terms of Jordan algebra generators is discussed. The key to the construction is the triality relation already incorporated into matrix products. A generalisation to Kac-Moody algebras in terms of vertex operators is proposed and may provide a clue for the construction of new representations of Kac-Moody algebras in terms of Jordan fields. © 1988.

Quantum algebraic description of the Moszkowski model

In this paper we investigate the behaviour of the Moukowski model within the mnten of quantum algebras. The Moszkwski Hamiltonian is diagonalized aractly for different numbers of panicles and for various values of the deformalion parameter of the quanlum algebra involved. We also include ranking in our system and observe its variation as a function of the deformation parameters. © 1992 IOP Publishing Ltd.

Further on the current algebra of WZNW models at and away from criticality

We comment on the off-critical perturbations of WZNW models by a mass term as well as by another descendent operator, when we can compare the results with further algebra obtained from the Dirac quantization of the model, in such a way that a more general class of models be included. We discover, in both cases, hidden Kac-Moody algebras obeyed by some currents in the off-critical case, which in several cases are enough to completely fix the correlation functions.

Updating QCD2

We review two-dimensional QCD. We start with the field theory aspects since 't Hooft's 1/N expansion, arriving at the non-Abelian bosonization formula, coset construction and gauge-fixing procedure. Then we consider the string interpretation, phase structure and the collective coordinate approach. Adjoint matter is coupled to the theory, and the Landau-Ginzburg generalization is analysed. We end with considerations concerning higher algebras, integrability, constraint structure, and the relation of high-energy scattering of hadrons with two-dimensional (integrable) field theories.

Fourier duality as a quantization principle

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally compact groups. Kac algebras - and the duality they incorporate - are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest nontrivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no longer complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Projective Fourier duality and Weyl quantization

The Weyl-Wigner correspondence prescription, which makes great use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. Both an Abelian and a symmetric projective Kac algebra are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.

Q-deformed fermionic Lipkin model at finite temperature

The interplay between temperature and q-deformation in the phase transition properties of many-body systems is studied in the particular framework of the collective q-deformed fermionic Lipkin model. It is shown that in phase transitions occuring in many-fermion systems described by su(2)q-like models are strongly influenced by the q-deformation.

Optimal clone identifier based on dynamic rules and process algebra

The rule creation to clone selection in different projects is a hard task to perform by using traditional implementations to control all the processes of the system. The use of an algebraic language is an alternative approach to manage all of system flow in a flexible way. In order to increase the power of versatility and consistency in defining the rules for optimal clone selection, this paper presents the software OCI 2 in which uses process algebra in the flow behavior of the system. OCI 2, controlled by an algebraic approach was applied in the rules elaboration for clone selection containing unique genes in the partial genome of the bacterium Bradyrhizobium elkanii Semia 587 and in the whole genome of the bacterium Xanthomonas axonopodis pv. citri. Copyright© (2009) by the International Society for Research in Science and Technology.

Algebraic approach to optimal clone selection applied in metagenomic projects

Due to the wide diversity of unknown organisms in the environment, 99% of them cannot be grown in traditional culture medium in laboratories. Therefore, metagenomics projects are proposed to study microbial communities present in the environment, from molecular techniques, especially the sequencing. Thereby, for the coming years it is expected an accumulation of sequences produced by these projects. Thus, the sequences produced by genomics and metagenomics projects present several challenges for the treatment, storing and analysis such as: the search for clones containing genes of interest. This work presents the OCI Metagenomics, which allows defines and manages dynamically the rules of clone selection in metagenomic libraries, thought an algebraic approach based on process algebra. Furthermore, a web interface was developed to allow researchers to easily create and execute their own rules to select clones in genomic sequence database. This software has been tested in metagenomic cosmid library and it was able to select clones containing genes of interest. Copyright 2010 ACM.

Construction of perfect space-time codes

In this work, we propose an innovative methodology to extend the construction of minimum and non-minimum delay perfect codes as a subset of cyclic division algebras over ℚ(ζ3), where the signal constellations are isomorphic to the hexagonal An 2 -rotated lattice, for any channel of any dimension n such that gcd{n, 3) = 1.

Quantificação econômica e energética em cultura de cana-de-açúcar na região da Alta paulista

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Modos de conceber a álgebra em cursos de formação de professores de matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Um modelo algébrico para a lógica do muito

Pós-graduação em Filosofia - FFC

Álgebras de Lie e aplicações à sistemas alternantes

Pós-graduação em Matemática - IBILCE