It is shown that Temperley-Lieb algebras in which the multiplicative generators satisfy hihi = nhi for n ≥ 2 can be isomorphically represented in matrices. Mathematics Subject Classification (2000): 57M99, 15A03, 16G99, 05C50

New emerging technologies in the field of multimedia, such as high dynamic range and wide color gamut, challenge the performance of existing image and video data processing algorithms, especially in terms of visual data compression and its faithful representation. High dynamic range and wide color gamut offer to capture and to represent a scene with extended amount of details in both, luminance...

A method is described to display faithfully on a CRT monitor the colours of images taken by a calibrated digital camera. A multicoloured ‘‘input’’ image, displayed on a monitor, was photographed with the camera. After correcting the digital image to take into account the gammas of both camera and monitor, the image was redisplayed as an ‘‘output’’ image on the same monitor. An iterative procedu...

LetG be the six dimensional linear algebraic k-group SL2(W2), where W2 is the ring of Witt vectors of length two over the algebraically closed field k of characteristic p > 0. Then the minimal dimension of a faithful rational krepresentation of G is p + 3.

We study the algebraic properties of the series Kn of semigroups, which is inspired by [Ki] and has origins in convexity theory. In particular, we describe Green’s relations on Kn, prove that there exists a faithful representation of Kn by n × n matrices with non-negative integer coefficients (and even explicitly construct such a representation), and prove that Kn does not admit a faithful repr...

We prove that, for a hyperbolic two-bridge knot, infinitely many Dehn fillings are rigid in SO0(4, 1). Here rigidity means that any discrete and faithful representation in SO0(4, 1) is conjugate to the holonomy representation in SO0(3, 1). We also show local rigidity for almost all Dehn fillings.