Related papers: The Space of Vector Fields on Q-Groups
We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…
The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and…
The tensor categories of oriented Kauffman diagrams are studied with description of fiber functors on them as well as the associated Hopf algebras.
Hopf algebra structure on the differential algebra of the extended $q$-plane is defined. An algebra of forms which is obtained from the generators of the extended $q$-plane is introduced and its Hopf algebra structure is given.
Starting from a recently-introduced algebraic structure on spin foam models, we define a Hopf algebra by dividing with an appropriate quotient. The structure, thus defined, naturally allows for a mirror analysis of spin foam models with…
A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed in q-alg/9609011 In this paper we give an outline of the construction of a noncommutative analogy of the algebra of partial…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
This paper works as an appendix of the paper titled Geometry of Associated Quantum Vector Bundles and the Quantum Gauge Group and for paper titled Yang-Mills-Connes Theory and Quantum Principal SU(N)-Bundles. Here, we are going to prove…
We show how topology of a space may lead to tensor fields on (the smooth part of) moduli spaces of the fundamental group.
We consider all possible dynamical theories which evolve two transverse vector fields out of a three-dimensional Euclidean hyperplane, subject to only two assumptions: (i) the evolution is local in space, and (ii) the theory is invariant…
Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…
Using Morita type stratifications, we establish a one-to-one correspondence between geometric vector fields on a separated differentiable stack and stratified vector fields on its orbit space. This correspondence enables us to derive a…
We establish a noncommutative analogue of the first fundamental theorem of classical invariant theory. For each quantum group associated with a classical Lie algebra, we construct a noncommutative associative algebra whose underlying vector…
We study a tentative generally covariant quantum field theory, denoted the T-Theory, as a tool to investigate the consistency of quantum general relativity. The theory describes the gravitational field and a minimally coupled scalar field;…
We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.
We explain the basic ideas, describe with proofs the main results, and demonstrate the effectiveness, of an evolving theory of vector-valued modular forms (vvmf). To keep the exposition concrete, we restrict here to the special case of the…
Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge…
In this paper we show that in the case of noncommutative two-tori one gets in a natural way simple structures which have analogous formal properties as Hopf algebra structures but with a deformed multiplication on the tensor product.