S. Paul Smith

Bezout's theorem for non-commutative projective spaces

We prove a version of B

Skew derivations andU q (sl(2))

ezout’s theorem for non-commutative analogues of the projective spaces P n . c 2001 Elsevier Science B.V. All rights reserved. MSC: 16W50; 16E10; 16E70

Curves on Quasi-Schemes

This note first describes the basic properties of the skew derivations on the polynomial ringk[X]. As a consequence of these properties it is proved that theq-analogue of the enveloping algebra of sl(2),Uq(sl(2)), has a unique action on C[X], where “action” means that C[X] is a module algebra in the Hopf algebra sense. This depends on the fact that the generators of a subalgebra ofUq(sl(2)) described by Woronowicz must act via an automorphism, and the skew derivations associated to it.

Maps between non-commutative spaces

AbstractThis paper concerns curves on noncommutative schemes, hereafter called quasi-schemes. Aquasi-scheme X is identified with the category

COMPUTATION OF THE GROTHENDIECK AND PICARD GROUPS OF A TORIC DM STACK BY USING A HOMOGENEOUS COORDINATE RING FOR

Mod{\text{ }}X

Noncommutative geometry of homogenized quantum (2, ℂ)

ofquasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embeddedhypersurface Y. Let C be a curve on X which is in ‘good position’ withrespect to Y (see Definition 5.1) – this definition includes a requirement that Xbe far from commutative in a certain sense. Then C is isomorphic to

Integral Non-commutative Spaces☆

\mathbb{V}_n^1