Related papers: Double-graded quantum superplane
Differential geometry of the quantum Lie superalgebra of the extended quantum superplane and its Z$_2$-graded Hopf algebra structure is obtained. Its Z$_2$-graded dual Hopf algebra is also given.
Super Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and…
In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum…
In this work, differential geometry of the Z$_3$-graded quantum superplane is constructed. The corresponding quantum Lie superalgebra and its Hopf algebra structure are obtained.
A quantum mechanical model that realizes the $ \mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is…
We show that the algebra of the bicovariant differential calculus on a quantum group can be understood as a projection of the cross product between a braided Hopf algebra and the quantum double of the quantum group. The resulting super-Hopf…
We define a new ${\mathbb Z}_2$-graded quantum (2+1)-space and show that the extended ${\mathbb Z}_2$-graded algebra of polynomials on this ${\mathbb Z}_2$-graded quantum space, denoted by ${\cal F}({\mathbb C}_q^{2\vert1})$, is a ${\mathbb…
We introduce a Z$_3$-graded quantum $(2+1)$-superspace and define Z$_3$-graded Hopf algebra structure on algebra of functions on the Z$_3$-graded quantum superspace. We construct a differential calculus on the Z$_3$-graded quantum…
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from \fun\ to \uqg\ , given by elements of the pure braid group. These operators --- the `reflection matrix' $Y \equiv…
We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO…
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given
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.
In this paper, we investigate certain graded-commutative rings which are related to the reciprocal plane compactification of the coordinate ring of a complement of a hyperplane arrangement. We give a presentation of these rings by…
We introduce a multiparametric quantum superspace with $m$ even generators and $n$ odd generators whose commutation relations are in the sense of Manin such that the corresponding algebra has a Hopf superalgebra. By using its Hopf…
We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of…
In this work, Z$_3$-graded quantum $(h,j)$-superplane is introduced with a help of proper singular $g$ matrix and a Z$_3$-graded calculus is constructed over this new $h$-superplane. A new Z$_3$-graded $(h,j)$-deformed quantum (super)group…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential…
We introduce a noncommutative differential calculus on the two-parameter $h$-superplane via a contraction of the (p,q)-superplane. We manifestly show that the differential calculus is covariant under $GL_{h_1,h_2}(1| 1)$ transformations. We…
It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on…