Given a (reduced) locally compact quantum group A, we can consider the convolution algebra L(A) (which can be identified as the predual of the von Neumann algebra form of A). It is conjectured that L(A) is operator biprojective if and only if A is compact. The “only if” part always holds, and the “if” part holds for Kac algebras. We show that if the splitting morphism associated with L(A) being...

Suppose S is a parametrized surface in complex projective 3-space P given as the image of φ : P ×P1 → P. The implicitization problem is to compute an implicit equation F = 0 of S using the parametrization φ. An algorithm using syzygies exists for computing F if φ has no base points, i.e. φ is everywhere defined. This work is an extension of this algorithm to the case of a surface with multiple ...

Amonge other things we give sufficient and necessary conditions for the Lau product of Banachalgebras to be biflat or biprojective.

In this paper, we study the approximate biprojectivity and biflatness of a Banach algebra A find some relations between theses concepts with ?-amenability ? -contractibility, where is character on A. Among other things, show that ?-Lau product L1(G) ?? A(G) approximately biprojective if only G finite, are group Fourier locally compact G, respectively. We also characterize biflat semigroup algeb...

amonge other things we give sufficient and necessary conditions for the lau product of banachalgebras to be biflat or biprojective.