Quantum supergroup structure of 1+1-dimensional quantum superplane, its dual and its differential calculus
نویسندگان
چکیده
We show that the 1 + 1-dimensional quantum superplane introduced by Manin is a quantum supergroup according to the Faddeev-Reshetikhin-Takhtajan approach. We give its supermatrix element, its corresponding R-matrix and its Hopf structure. This new point of view allows us, first, to realize its dual Hopf superalgebra starting from postulated initial pairings. Second, we construct a right-invariant differential calculus on it and then deduce the corresponding quantum Lie superalgebra which as a commutation super-algebra appears classical, and as Hopf structure is a non-cocommutative q-deformed one. An isomorphism between the latter and the dual one obtained in the first method is given. E-mail:[email protected] E-mail: [email protected] Permanent address
منابع مشابه
On the Differential Geometry of GLq(1|1)
The differential calculus on the quantum supergroup GLq(1|1) was introduced by Schmidke et al. (1990 Z. Phys. C 48 249). We construct a differential calculus on the quantum supergroup GLq(1|1) in a different way and we obtain its quantum superalgebra. The main structures are derived without an R-matrix. It is seen that the found results can be written with help of a matrix R̂ 1 E-mail: scelik@fe...
متن کاملCartan Calculi On The Quantum Superplane
Cartan calculi on the extended quantum superplane are given. To this end, the noncommutative differential calculus on the extended quantum superplane is extended by introducing inner derivations and Lie derivatives. E-mail: [email protected]
متن کاملDifferential geometry of the Z3-graded quantum superplane
In this work, differential geometry of the Z3-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained. E-mail: [email protected]
متن کاملSupersymmetrizing Landau Models
This is an overview of recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in the uniform magnetic field, as well as of its Haldane’s S2 generalization (hep-th/0311159, 0404108, 0510019, 0612300). The main attention is paid to the planar super Landau models which are invariant under the inhomogeneous supergroup ISU(1|1), a contract...
متن کاملWhen the classical & quantum mechanical considerations hint to a single point; a microscopic particle in a one dimensional box with two infinite walls and a linear potential inside it
In this paper we have solved analytically the Schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. Based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999