Noncommutative Curves Of Genus Zero
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Noncommutative Curves of Genus Zero
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Author | : Dirk Kussin |
Publsiher | : American Mathematical Society(RI) |
Total Pages | : 146 |
Release | : 2014-09-11 |
Genre | : MATHEMATICS |
ISBN | : 1470405563 |
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Noncommutative Curves of Genus Zero
Author | : Dirk Kussin |
Publsiher | : American Mathematical Soc. |
Total Pages | : 147 |
Release | : 2024 |
Genre | : Mathematics |
ISBN | : 9780821866832 |
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Noncommutative Curves of Genus Zero
Author | : Dirk Kussin |
Publsiher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 2009-08-07 |
Genre | : Mathematics |
ISBN | : 9780821844007 |
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In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Symplectic Poisson and Noncommutative Geometry
Author | : Tohru Eguchi,Yakov Eliashberg,Yoshiaki Maeda |
Publsiher | : Cambridge University Press |
Total Pages | : 303 |
Release | : 2014-08-25 |
Genre | : Mathematics |
ISBN | : 9781107056411 |
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This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute.
Operator Theory on Noncommutative Domains
Author | : Gelu Popescu |
Publsiher | : American Mathematical Soc. |
Total Pages | : 137 |
Release | : 2010 |
Genre | : Dilation theory (Operator theory). |
ISBN | : 9780821847107 |
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"Volume 205, number 964 (third of 5 numbers)."
Noncommutative Differential Geometry and Its Applications to Physics
Author | : Yoshiaki Maeda,Hitoshi Moriyoshi,Hideki Omori,Daniel Sternheimer,Tatsuya Tate,Satoshi Watamura |
Publsiher | : Springer Science & Business Media |
Total Pages | : 310 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9789401007047 |
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Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.
Points and Curves in the Monster Tower
Author | : Richard Montgomery,Mikhail Zhitomirski_ |
Publsiher | : American Mathematical Soc. |
Total Pages | : 154 |
Release | : 2010-01-15 |
Genre | : Mathematics |
ISBN | : 9780821848180 |
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Cartan introduced the method of prolongation which can be applied either to manifolds with distributions (Pfaffian systems) or integral curves to these distributions. Repeated application of prolongation to the plane endowed with its tangent bundle yields the Monster tower, a sequence of manifolds, each a circle bundle over the previous one, each endowed with a rank $2$ distribution. In an earlier paper (2001), the authors proved that the problem of classifying points in the Monster tower up to symmetry is the same as the problem of classifying Goursat distribution flags up to local diffeomorphism. The first level of the Monster tower is a three-dimensional contact manifold and its integral curves are Legendrian curves. The philosophy driving the current work is that all questions regarding the Monster tower (and hence regarding Goursat distribution germs) can be reduced to problems regarding Legendrian curve singularities.
Two Kinds of Derived Categories Koszul Duality and Comodule Contramodule Correspondence
Author | : Leonid Positselski |
Publsiher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 2011 |
Genre | : Comodules |
ISBN | : 9780821852965 |
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"July 2011, volume 212, number 996 (first of 4 numbers)."