Cluster Algebras And Poisson Geometry

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Cluster Algebras And Poisson Geometry

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Author : Michael Gekhtman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Cluster Algebras And Poisson Geometry written by Michael Gekhtman 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 2010 with Mathematics categories.

The first book devoted to cluster algebras, this work contains chapters on Poisson geometry and Schubert varieties; an introduction to cluster algebras and their main properties; and geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.

Cluster Algebras And Poisson Geometry

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Author : Michael Gekhtman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-01-01

Cluster Algebras And Poisson Geometry written by Michael Gekhtman 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 2010-01-01 with Mathematics categories.

Advances In Poisson Geometry

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Author : Mario Garcia-Fernandez
language : en
Publisher: Springer Nature
Release Date : 2025-08-24

Advances In Poisson Geometry written by Mario Garcia-Fernandez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-24 with Mathematics categories.

This book presents recent advances in topics related to Poisson geometry originating from lectures given at the “Poisson School” held in 2022 at the CRM in Barcelona. The purpose is to give both an introduction to this active field of research as well as highlight new trends in related topics. The texts cover both classical results, known to experts in the field, as well as recent and previously unpublished mathematical results. Graduate students and early-stage researchers with basic knowledge in differential and symplectic geometry, together with established researchers that are keen to dive into this rapidly growing field of research, will find this book a useful resource.

Algebraic Geometry And Number Theory

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Author : victor ginzburg
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

Algebraic Geometry And Number Theory written by victor ginzburg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-31 with Mathematics categories.

This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld. Original research articles reflect the range of Drinfeld's work, and his profound contributions to the Langlands program, quantum groups, and mathematical physics are paid particular attention. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.

Cluster Algebra Structures On Poisson Nilpotent Algebras

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Author : K. R Goodearl
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-27

Cluster Algebra Structures On Poisson Nilpotent Algebras written by K. R Goodearl and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.

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Lectures On Poisson Geometry

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Author : Marius Crainic
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-10-14

Lectures On Poisson Geometry written by Marius Crainic 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 2021-10-14 with Education categories.

This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto

Cluster Algebras And Triangulated Surfaces Part Ii Lambda Lengths

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Author : Sergey Fomin
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-03

Cluster Algebras And Triangulated Surfaces Part Ii Lambda Lengths written by Sergey Fomin 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 2018-10-03 with Mathematics categories.

For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, the authors construct a geometric realization in terms of suitable decorated Teichmüller space of the surface. On the geometric side, this requires opening the surface at each interior marked point into an additional geodesic boundary component. On the algebraic side, it relies on the notion of a non-normalized cluster algebra and the machinery of tropical lambda lengths. The authors' model allows for an arbitrary choice of coefficients which translates into a choice of a family of integral laminations on the surface. It provides an intrinsic interpretation of cluster variables as renormalized lambda lengths of arcs on the surface. Exchange relations are written in terms of the shear coordinates of the laminations and are interpreted as generalized Ptolemy relations for lambda lengths. This approach gives alternative proofs for the main structural results from the authors' previous paper, removing unnecessary assumptions on the surface.

Quantum Cluster Algebra Structures On Quantum Nilpotent Algebras

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Author : K. R. Goodearl
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25

Quantum Cluster Algebra Structures On Quantum Nilpotent Algebras written by K. R. Goodearl 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 2017-04-25 with Mathematics categories.

All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts

Symmetries And Integrability Of Difference Equations

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Author : Decio Levi
language : en
Publisher: Springer
Release Date : 2017-06-30

Symmetries And Integrability Of Difference Equations written by Decio Levi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-30 with Science categories.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification

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Author : Jacob Greenstein
language : en
Publisher: Springer Nature
Release Date : 2022-03-11

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification written by Jacob Greenstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Mathematics categories.

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.