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Cluster Algebras and Poisson Geometry
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.
A Plethora of Cluster Structures on $GL_n$
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Exotic Cluster Structures on $SL_n$: The Cremmer-Gervais Case
This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson–Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin–Drinfeld classification of Poisson–Lie structures on corresponds to a cluster structure in . The authors have shown before that this conjecture holds for any in the case of the standard Poisson–Lie structure and for all Belavin–Drinfeld classes in , . In this paper the authors establish it for the Cremmer–Gervais Poisson–Lie structure on , which is the least similar to the standard one.
Representations and Nilpotent Orbits of Lie Algebraic Systems
This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.
Controllable Quantum States: Mesoscopic Superconductivity And Spintronics (Ms+s2006) - Proceedings Of The International Symposium
This volume is a collection of papers from the fourth meeting of the International Symposium on Mesoscopic Superconductivity and Spintronics held at NTT Atsugi, Japan. Research in these fields has advanced a great deal since the previous meeting, largely because these fields have drawn much attention from the viewpoint of new quantum phenomena and quantum information technology. Mesoscopic superconductivity has been developed in new fields, such as a ferromagnet/superconductor junction, the proximity effect in unconventional superconductors, macroscopic quantum tunneling in high-Tc superconductors, quantum modulation of superconducting junctions and superconducting quantum bits. The book also covers transport and spins in nano-scale semiconductor structures such as quantum dots and wires, quantum interference and coherence and order in exotic materials, and some papers on quantum algorithm. This book adequately provides an overview of recent progress in mesoscopic superconductivity.
Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
From Field Theory to Quantum Groups
Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.
Controllable Quantum States
This volume is a collection of papers from the fourth meeting of the International Symposium on Mesoscopic Superconductivity and Spintronics held at NTT Atsugi, Japan. Research in these fields has advanced a great deal since the previous meeting, largely because these fields have drawn much attention from the viewpoint of new quantum phenomena and quantum information technology. Mesoscopic superconductivity has been developed in new fields, such as a ferromagnet/superconductor junction, the proximity effect in unconventional superconductors, macroscopic quantum tunneling in high-Tc superconductors, quantum modulation of superconducting junctions and superconducting quantum bits. The book also covers transport and spins in nano-scale semiconductor structures such as quantum dots and wires, quantum interference and coherence and order in exotic materials, and some papers on quantum algorithm. This book adequately provides an overview of recent progress in mesoscopic superconductivity.
