The Differential Calculus on Quantum Linear Groups
نویسندگان
چکیده
The non-commutative differential calculus on the quantum groups SL q (N) is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the constructive way obeys the modified version of the Leibnitz rules.
منابع مشابه
3 v 1 1 9 N ov 1 99 2 GL q ( N ) - Covariant Quantum Algebras and Covariant Differential Calculus ∗
We consider GL q (N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrari-ness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is dissc...
متن کاملGinsburg-Pitaevski-Gross differential equation with the Rosen-Morse and modified Woods-Saxon potentials
In this paper, we consider non-linear Ginsburg-Pitaevski-Gross equation with the Rosen-Morse and modifiedWoods-Saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. We use the Runge- Kutta-Fehlberg approximation method to solve the resulting non-linear equation.
متن کاملImplications of the Hopf Algebra Properties of Noncommutative Differential Calculi
We define a noncommutative algebra of four basic objects within a differential calculus on quantum groups – functions, 1-forms, Lie derivatives, and inner derivations – as the crossproduct algebra associated with Woronowicz’s (differential) algebra of functions and forms. This definition properly takes into account the Hopf algebra structure of the Woronowicz calculus. It also provides a direct...
متن کاملThe Problem of Differential Calculus on Quantum Groups
The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus which arises from a simple quantum Lie algebra lh(g). This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisf...
متن کاملAn analytic study on the Euler-Lagrange equation arising in calculus of variations
The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...
متن کامل