Differential Geometry of the q-superplane
نویسنده
چکیده
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which is obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given. E-mail: [email protected] New E-mail address: [email protected]
منابع مشابه
Differential 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 کاملQuantum supergroup structure of 1+1-dimensional quantum superplane, its dual and its differential calculus
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-invaria...
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 کاملar X iv : q - a lg / 9 51 10 09 v 2 1 7 D ec 1 99 5 h - deformation of GL ( 1 | 1 )
h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.
متن کاملDifferential Geometry of the Lie Superalgebra of the Quantum Superplane
Noncommutative differential geometry has attracted considerable interest both mathematically and also from theoretical physics side over the past decade. Especially, there is much activity in differential geometry on quantum groups. For references to the literature for quantum groups we refer to the recent book by Majid [1]. The basic structure giving a direction to the noncommutative geometry ...
متن کامل