7 citations · 15 across the 5 of their papers we have counts for
5 papers
On bialgebras associated with paths and essential paths on ADE graphs
Robert Coquereaux, Ariel O. Garcia
We define a graded multiplication on the vector space of essential paths on a graph (a tree) and show that it is associative. In most interesting applications, this tree is an…
Integrable models and star structures
Ariel O. Garcia, Roberto C. Trinchero
We consider the representations of Hopf algebras involved in some physical models, namely, factorizable S-matrix models (FSM's), one-dimensional quantum spin chains (QSC's) and sta…
Associated quantum vector bundles and symplectic structure on a quantum plane
R. Coquereaux, A. O. Garcia, R. Trinchero
We define a quantum generalization of the algebra of functions over an associated vector bundle of a principal bundle. Here the role of a quantum principal bundle is played by a Ho…
Finite dimensional quantum group covariant differential calculus on a complex matrix algebra
R. Coquereaux, A. O. Garcia, R. Trinchero
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken as a reduced quantum plane, we build a differential calculus Omega(S) on the quantum space S defined b…
Constructive building of the Lax pair in the non-linear sigma model
Ariel O. Garcia, Roberto C. Trinchero
A derivation of the Lax pair for the (1+1)-dimensional non-linear sigma-model is described. Its main benefit is to have a clearer physical origin and to allow the study of a genera…