73 citations · 2.5k across the 138 of their papers we have counts for
11 papers · 1 filter
Solutions for the constant quantum Yang-Baxter equation from Lie (super)algebras
A. Tanasa, A. Ballesteros, F. J. Herranz
We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired in the Lie (super)algebr…
New time-type and space-type non-standard quantum algebras and discrete symmetries
Francisco J. Herranz
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so…
Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
A. Ballesteros, F. J. Herranz, J. Negro +1
The minimal twist map introduced by B. Abdesselam, A. Chakrabarti, R. Chakrabarti and J. Segar (Mod. Phys. Lett. A 14 (1999) 765) for the non-standard (Jordanian) quantum sl(2,R) a…
A new quantum so(2,2) algebra
Francisco J. Herranz
By starting from the non-standard quantum deformation of the sl(2,R) algebra, a new quantum deformation for the real Lie algebra so(2,2) is constructed by imposing the former to be…
Two-photon algebra deformations
Preeti Parashar, Angel Ballesteros, Francisco J. Herranz
In order to obtain a classification of all possible quantum deformations of the two-photon algebra , we introduce its corresponding general Lie bialgebra, which is a coboundar…
Integrable deformations of Hamiltonian systems and q-symmetries
Angel Ballesteros, Francisco J. Herranz
The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2,R) coalgebra sy…
(1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
Angel Ballesteros, Francisco J. Herranz, Preeti Parashar
All Lie bialgebra structures for the (1+1)-dimensional centrally extended Schrodinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all o…
Quantum (1+1) extended Galilei algebras: from Lie bialgebras to quantum R-matrices and integrable systems
Angel Ballesteros, Enrico Celeghini, Francisco J. Herranz
The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and classified into four multiparametric families. Their quantum deformations are obtained, together with the…
Quantum harmonic oscillator algebras as non-relativistic limits of multiparametric quantizations
Angel Ballesteros, Francisco J. Herranz, Preeti Parashar
Multiparametric quantum algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit le…
On quantum algebra symmetries of discrete Schrödinger equations
Angel Ballesteros, Francisco J. Herranz, Javier Negro +1
Two non-standard quantum deformations of the (1+1) Schrödinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Sch…
Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
Angel Ballesteros, Francisco J. Herranz, Preeti Parashar
Multiparametric quantum deformations of are studied through a complete classification of Lie bialgebra structures. From them, the non-relativistic limit leading to…