10,307 research outputs found
Full centre of an H -module algebra
We apply the full centre construction, defined in arXiv:0908.1250, to
algebras in and module categories over categories of representations of Hopf
algebras. We obtain a compact formula for the full centre of a module algebra
over a Hopf algebra
Error bound for radial basis interpolation in terms of a growth function
We suggest an improvement of Wu-Schaback local error bound for radial basis interpolation by using a polynomial growth function. The new bound is valid without any assumptions about the density of the interpolation centers. It can be useful for the localized methods of scattered data fitting and for the meshless discretization of partial differential equation
Algorithms and error bounds for multivariate piecewise constant approximation
We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree approximation, as well as recent results about approximation orders achievable on anisotropic partitions
Nuclei of categories with tensor products
Following the analogy between algebras (monoids) and monoidal categories the
construction of nucleus for non-associative algebras is simulated on the
categorical level. Nuclei of categories of modules are considered as an
example
Pentagon equation and matrix bialgebras
We classify coproducts on matrix algebra in terms of solutions to some
modification of pentagon equation. The construction of Baaj and Skandalis
describing finite dimensional unitary solutions of pentagon equation is
extended to the non-unitary case. We establish the relation between Hopf-Galois
algebras and solutions to modified pentagon equation.Comment: 21 page
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