Related papers: q-Epsilon tensor for quantum and braided spaces
In a recent paper the quantum 2-sphere $S^2_q$ was described as a quantum complex manifold. Here we consider several copies of $S^2_q$ and derive their braiding commutation relations. The braiding is extended to the differential and to the…
For a quasitriangular C*-quantum group, we enrich the twisted tensor product constructed in the first part of this series to a monoidal structure on the category of its continuous coactions on C*-algebras. We define braided C*-quantum…
We construct a braided structure on the algebra of K\"ahler differential forms of a commutative algebra twisted by an endomorphism. This generalises the construction done in M. Karoubi, Quantum Methods in Algebraic Topology, see…
We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge5$ so that at each point of $M$ the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes…
We introduce a definition of braided tensor product $\operatorname{M}\overline{\boxtimes}\operatorname{N}$ of von Neumann algebras equipped with an action of a quasi-triangular quantum group $\mathbb{G}$ (this includes the case when…
We describe how to find quantum determinants and antipode formulas from braided vector spaces using the FRT-construction and finite-dimensional Nichols algebras. It generalizes the construction of quantum function algebras using quantum…
Let $(\mathrm{U},\mathrm{U}^\imath)$ be the quantum symmetric pair of arbitrary finite type and $G^*$ be the associated dual Poisson-Lie group. Generalizing the work of De Concini and Procesi, the first author introduced an integral form…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
We demonstrate our recent general results on the Casimir construction and moduli space of all bicovariant calculi by means of some detailed examples, including finite-difference and 2-jet cacluli on $\R^n$ and full details of the Casimir…
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
We write the fermionic $q$-Fock space representation of $U_q(\hat{sl_n})$ as an infinite extended braided tensor product of finite-dimensional fermionic $U_q(sl_n)$-quantum planes or exterior algebras. Using braided geometrical techniques…
We construct analogs of the Gelfand-Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the quantum groups U_q(sl(N)). Corresponding semiclassical (i.e. Poisson) counterparts…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
We construct noncommutative `Riemannian manifold' structures on dual quasitriangular Hopf algebras such as $C_q[SU_2]$ with its standard bicovariant differential calculus, using the quantum frame bundle formalism introduced previously. The…
An embedding method to get $q$-deformations for the non--semisimple algebras generating the motion groups of $N$--dimensional flat spaces is presented. This method gives a global and simultaneous scheme of $q$-deformation for all $iso(p,q)$…
Let V be the 7-dimensional irreducible representation of the quantum group U_q(g_2). For each n, there is a map from the braid group B_n to the endomorphism algebra of the n-th tensor power of V, given by R-matrices. We can extend this…
We work out a theory of integrability on the braided covector Hopf algebra and braided vector Hopf algebra of type A_n as introduced by Kempf and Majid. Starting by their definition of braided Fourier transform we prove n-dimensional…
A ${\mathbb Z}_2$-graded qubit represents an even (bosonic) "vacuum state" and an odd, excited, Majorana fermion state. The multiparticle sectors of $N$, braided, indistinguishable Majorana fermions are constructed via first quantization.…