𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Center of Some Quantum Projective Planes

✍ Scribed by Izuru Mori

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
209 KB
Volume
204
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

The homogeneous coordinate ring of a quantum projective plane is a 3-dimensional Artin᎐Schelter regular algebra with the same Hilbert series as the polynomial ring in three variables; such an algebra A is a graded noncommutative analogue of the polynomial ring in three variables. When A is a finite module over Ž . Ž Ž .. its center Z A , we define the scheme S s Proj Z A and the sheaf A A of Ž .

and following Grothendieck we may define the scheme Spec Z Z . The 0 algebras A fall into several families, and for many of these it has been shown that Ε½ .

2

Ε½ . Spec Z Z ( ‫ސ‬ when A is finite over its center. This paper shows that Spec Z Z ( ‫ސ‬ 2 for two more families.

πŸ“œ SIMILAR VOLUMES

On the Number of Cyclic Projective Plane
On the Number of Cyclic Projective Planes
✍ John Konvalina πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 141 KB

An explicit formula for the number of finite cyclic projective planes or planar . Ε½ . difference sets is derived by applying Ramanujan sums Von Sterneck numbers and Mobius inversion over the set partition lattice to counting one-to-one solution vectors of multivariable linear congruences.

Hyperovals in the known projective plane
Hyperovals in the known projective planes of order 16
✍ Tim Penttila; Gordon F. Royle; Michael K. Simpson πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 382 KB

We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.

Classification of Embeddings of the Flag
Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 1
✍ Joseph A. Thas; Hendrik Van Maldeghem πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 156 KB

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse conta

Classification of Embeddings of the Flag
Classification of Embeddings of the Flag Geometries of Projective Planes in Finite Projective Spaces, Part 3
✍ Joseph A. Thas; Hendrik Van Maldeghem πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 214 KB

The flag geometry 1=(P, L, I) of a finite projective plane 6 of order s is the generalized hexagon of order (s, 1) obtained from 6 by putting P equal to the set of all flags of 6, by putting L equal to the set of all points and lines of 6, and where I is the natural incidence relation (inverse conta

Generating even triangulations of the pr
Generating even triangulations of the projective plane
✍ Yusuke Suzuki; Takahiro Watanabe πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 255 KB

## Abstract We shall determine the 20 families of irreducible even triangulations of the projective plane. Every even triangulation of the projective plane can be obtained from one of them by a sequence of __even‐splittings__ and __attaching octahedra__, both of which were first given by Batagelj 2