Introduction to Quantum Groups

Чайчиан, Масуд; Demichev, Andrey

doi:10.1142/3065

Cited by 130 publications

(144 citation statements)

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“…= [1] q [2] q [3] q Á Á Á[n À 1] q [n] q , [n] q = (1 À q n )/(1 À q) and the subscript outside the square bracket denotes the q-deformed version of the argument inside the square bracket. It is clear from the above expressions that under the limit q ?…”

Section: The Q-deformation Of Nonlinear Mapsmentioning

confidence: 99%

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A comparative study on the co-existing attractors in the Gaussian map and its q-deformed version

Patidar

Sud

2009

Communications in Nonlinear Science and Numerical Simulation

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Section: The Q-deformation Of Nonlinear Mapsmentioning

confidence: 99%

“…(i.e. the q-mathematics) [1]. The q-deformation of any function is to introduce an additional parameter (q) in the definition of function in such a way that under the limit q ?…”

Section: Introductionmentioning

confidence: 99%

A comparative study on the co-existing attractors in the Gaussian map and its q-deformed version

Patidar

Sud

2009

Communications in Nonlinear Science and Numerical Simulation

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“…2 6 For this relation and its environment we suggest to take a look at [2,4,5,9], as a choice of various sorts. 7 This formula appears in [3] as formula (35) Fortunately, like in the q = 1 case, the converse is true as well though the proof requires more subtle arguments than the standard ones for q = 1.…”

Section: Proposition 9 Suppose S Has Invariant Domain If S Has a Q-mentioning

confidence: 99%

q-positive definiteness and related operators

Ôta

Szafraniec

2007

Journal of Mathematical Analysis and Applications

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We are in progress of extending the family of 'q-deformed operators' considered in the previous papers by joining to them q-subnormal as well as q-formally subnormal ones. It turns out that q-positive definiteness, a notion generalizing Halmos' standard positive definiteness of bounded subnormal operators, is likewise central for our new scheme. A few words of introductionSubnormal, quasinormal and hyponormal are the most favoured normal-like bounded operators. In the unbounded case the family turns out to be richer if besides (a) normal, subnormal and hyponormal operators; one allows to consider (b) formally normal and formally subnormal ones

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“…The purpose of this paper is to report a q-deformation ([6 8], review article [9]) of the bi-local system characterized by a relativistic harmonic-oscillator potential. We can show that such a system has a good convergence property, [10], in one-loop level.…”

Section: Introductionmentioning

confidence: 99%

Onq-deformation of bi-local system

2006

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We study a way of q-deformation of the bi-local system, the two-particle system bounded by a relativistic harmonic-oscillator type of potential, from both points of view of mass spectra and the behavior of scattering amplitudes. In our formulation, the deformation is done so that p2 the square of center-of-mass momentum, enters into the deformation parameters of relative coordinates. As a result, the wave equation of the bilocal system becomes nonlinear with respect to p2; then, the propagator of the bi-local system suffers significant change so as to get a convergent self energy to the second order. The study is also made on the covariant q-deformation in four-dimensional spacetime.

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Introduction to Quantum Groups

Cited by 130 publications

References 0 publications

A comparative study on the co-existing attractors in the Gaussian map and its q-deformed version

A comparative study on the co-existing attractors in the Gaussian map and its q-deformed version

q-positive definiteness and related operators

Onq-deformation of bi-local system

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