Related papers: The Jordanian Bicovariant Differential Calculus
Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne-Mumford stacks with projective coarse moduli spaces. We prove a formula for orbifold Gromov-Witten invariants of the product stack $\mathcal{X}_1\times \mathcal{X}_2$ in terms…
Let $\mathcal A$ and $\mathcal B$ be unital rings and $\mathcal M$ be a $(\mathcal A, \mathcal B)$-bimodule, which is faithful as a left $\mathcal A$-module and also as a right $\mathcal B$-module. Let ${\mathcal U}={\rm Tri}(\mathcal A,…
Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation…
We determine couples of singular moduli which have rational products
Determining the Jordan canonical form of the tensor product of Jordan blocks has many applications including to the representation theory of algebraic groups, and to tilting modules. Although there are several algorithms for computing this…
We consider Hopf bimodules and crossed modules over a Hopf algebra $H$ in a braided category. They are the key-stones for braided bicovariant differential calculi and their invariant vector fields respectively, as well as for the…
The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The…
Brylawski's tensor product formula expresses the Tutte polynomial of the tensor product of two graphs in terms of Tutte polynomials arising from the tensor factors. We are concerned with extensions of Brylawski's tensor product formula to…
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…
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in points of some domain, where the polynomial is assumed to have sup norm at most 1. One method, due to…
We present the star-product algebra of the kappa-deformation of Minkowski space and the formulation of Poincare covariant differential calculus. We use these tools to construct a twisted K-cycle over the algebra and a twisted cyclic…
The differential calculus on n-dimensional quantum Minkowski space covariant with respect to left action of Kappa-Poincar'e group is constructed and its uniqueness is shown.
The fundamental Davis-Januszkiewicz construction of toric manifolds is reinterpreted in order to allow for generalization. Applications involve the simplicial wedge $J$-construction and Ayzenberg's recent identities arising from composed…
Fourdimensional bicovariant differential calculus on quantum E(2) group is constructed.
We construct a sixth order differential equation having the central extension of $C_2$ by the Hall-Janko group $J_2$ as monodromy group. Moreover it arises from an iterated application of tensor products and convolution operations from a…
We provide the Cartan calculus for bicovariant differential forms on bicrossproduct quantum groups $k(M)\lrbicross kG$ associated to finite group factorizations $X=GM$ and a field $k$. The irreducible calculi are associated to certain…
A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.
We compute the simple finite-dimensional modules and the center of the Drinfeld double of the Jordan plane introduced in $\texttt{arXiv:2002.02514}$ assuming that the characteristic is zero.
We propose a new generalisation of the Jordanian twist (building on the previous idea from [Meljanac S., Meljanac D., Pachol A., Pikutic D., J. Phys. A: Math. Theor. 50 (2017), 265201, 11 pages]). Obtained this way, the family of the…
We define a notion of tensor product of bimodule categories and prove that with this product the 2-category of C-bimodule categories for fixed tensor C is a monoidal 2-category in the sense of Kapranov and Voevodsky. We then provide a…