On Dynamical Poisson Groupoids I

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On Dynamical Poisson Groupoids I

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Author : Luen-Chau Li
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

On Dynamical Poisson Groupoids I written by Luen-Chau Li and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors.

On Dynamical Poisson Groupoids

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Author : Luen-Chau Li
language : en
Publisher:
Release Date : 2005

On Dynamical Poisson Groupoids written by Luen-Chau Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups

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Author : Jie Wu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

On Maps From Loop Suspensions To Loop Spaces And The Shuffle Relations On The Cohen Groups written by Jie Wu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

The maps from loop suspensions to loop spaces are investigated using group representations in this article. The shuffle relations on the Cohen groups are given. By using these relations, a universal ring for functorial self maps of double loop spaces of double suspensions is given. Moreover the obstructions to the classical exponent problem in homotopy theory are displayed in the extension groups of the dual of the important symmetric group modules Lie$(n)$, as well as in the top cohomology of the Artin braid groups with coefficients in the top homology of the Artin pure braid groups.

Equivalences Of Classifying Spaces Completed At The Prime Two

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Author : Robert Oliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Equivalences Of Classifying Spaces Completed At The Prime Two written by Robert Oliver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

We prove here the Martino-Priddy conjecture at the prime $2$: the $2$-completions of the classifying spaces of two finite groups $G$ and $G'$ are homotopy equivalent if and only if there is an isomorphism between their Sylow $2$-subgroups which preserves fusion. This is a consequence of a technical algebraic result, which says that for a finite group $G$, the second higher derived functor of the inverse limit vanishes for a certain functor $\mathcal{Z}_G$ on the $2$-subgroup orbit category of $G$. The proof of this result uses the classification theorem for finite simple groups.

Quantum Groups And Lie Theory

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Author : Andrew Pressley
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-17

Quantum Groups And Lie Theory written by Andrew Pressley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-17 with Mathematics categories.

Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.

The Beilinson Complex And Canonical Rings Of Irregular Surfaces

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Author : Alberto Canonaco
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

The Beilinson Complex And Canonical Rings Of Irregular Surfaces written by Alberto Canonaco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

An important theorem by Beilinson describes the bounded derived category of coherent sheaves on $\mathbb{P n$, yielding in particular a resolution of every coherent sheaf on $\mathbb{P n$ in terms of the vector bundles $\Omega {\mathbb{P n j(j)$ for $0\le j\le n$. This theorem is here extended to weighted projective spaces. To this purpose we consider, instead of the usual category of coherent sheaves on $\mathbb{P ({\rm w )$ (the weighted projective space of weights $\rm w=({\rm w 0,\dots,{\rm w n)$), a suitable category of graded coherent sheaves (the two categories are equivalent if and only if ${\rm w 0=\cdots={\rm w n=1$, i.e. $\mathbb{P ({\rm w )= \mathbb{P n$), obtained by endowing $\mathbb{P ({\rm w )$ with a natural graded structure sheaf. The resulting graded ringed space $\overline{\mathbb{P ({\rm w )$ is an example of graded scheme (in chapter 1 graded schemes are defined and studied in some greater generality than is needed in the rest of the work). Then in chapter 2 we prove This weighted version of Beilinson's theorem is then applied in chapter 3 to prove a structure theorem for good birational weighted canonical projections of surfaces of general type (i.e., for morphisms, which are birational onto the image, from a minimal surface of general type $S$ into a $3$-dimensional $\mathbb{P ({\rm w )$, induced by $4$ sections $\sigma i\in H0(S,\mathcal{O S({\rm w iK S))$). This is a generalization of a theorem by Catanese and Schreyer (who treated the case of projections into $\mathbb{P 3$), and is mainly interesting for irregular surfaces, since in the regular case a similar but simpler result (due to Catanese) was already known. The theorem essentially states that giving a good birational weighted canonical projection is equivalent to giving a symmetric morphism of (graded) vector bundles on $\overline{\mathbb{P ({\rm w )$, satisfying some suitable conditions. Such a morphism is then explicitly determined in chapter 4 for a family of surfaces with numerical invariant

Quasi Ordinary Power Series And Their Zeta Functions

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Author : Enrique Artal-Bartolo
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Quasi Ordinary Power Series And Their Zeta Functions written by Enrique Artal-Bartolo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Intends to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, this title computes the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h, T)$ of a quasi-ordinary power series $h$ of arbitrary dimension

The Complex Monge Ampere Equation And Pluripotential Theory

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Author : Sławomir Kołodziej
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

The Complex Monge Ampere Equation And Pluripotential Theory written by Sławomir Kołodziej and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

We collect here results on the existence and stability of weak solutions of complex Monge-Ampere equation proved by applying pluripotential theory methods and obtained in past three decades. First we set the stage introducing basic concepts and theorems of pluripotential theory. Then the Dirichlet problem for the complex Monge-Ampere equation is studied. The main goal is to give possibly detailed description of the nonnegative Borel measures which on the right hand side of the equation give rise to plurisubharmonic solutions satisfying additional requirements such as continuity, boundedness or some weaker ones. In the last part, the methods of pluripotential theory are implemented to prove the existence and stability of weak solutions of the complex Monge-Ampere equation on compact Kahler manifolds. This is a generalization of the Calabi-Yau theorem.

Weil Petersson Metric On The Universal Teichmuller Space

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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Weil Petersson Metric On The Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).

A Random Tiling Model For Two Dimensional Electrostatics

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Author : Mihai Ciucu
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

A Random Tiling Model For Two Dimensional Electrostatics written by Mihai Ciucu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Studies the correlation of holes in random lozenge (i.e., unit rhombus) tilings of the triangular lattice. This book analyzes the joint correlation of these triangular holes when their complement is tiled uniformly at random by lozenges.