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Author : Bangming Deng,Jie Du,Qiang Fu
Publisher : Cambridge University Press
Page : 217 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781107608603
The first book of its kind to present an algebraic approach to affine q-Schur algebras and affine quantum Schur-Weyl theory.
Author : Bangming Deng,Jie Du,Qiang Fu
Publisher : Cambridge University Press
Page : 217 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781139789936
The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality.
Author : Zhaobing Fan,Chun-Ju Lai,Yiqiang Li,Li Luo,Weiqiang Wang
Publisher : American Mathematical Society
Page : 108 pages
File Size : 46,9 Mb
Release : 2023-01-18
Category : Mathematics
ISBN : 9781470456269
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Author : Srikanth B. Iyengar,Graham J. Leuschke,Anton Leykin,Claudia Miller,Ezra Miller,Anurag K. Singh,Uli Walther
Publisher : American Mathematical Society
Page : 108 pages
File Size : 42,8 Mb
Release : 2022-07-19
Category : Mathematics
ISBN : 9781470471590
This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Author : Wolfgang Metzler,Stephan Rosebrock
Publisher : Cambridge University Press
Page : 193 pages
File Size : 55,6 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316600900
Presents the current state of knowledge in all aspects of two-dimensional homotopy theory. Useful for both students and experts.
Author : David Jordan,Nadia Mazza,Sibylle Schroll
Publisher : Cambridge University Press
Page : 407 pages
File Size : 55,9 Mb
Release : 2023-08-17
Category : Mathematics
ISBN : 9781009097352
Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.
Author : Jie Du,Jianpan Wang,Lei Lin
Publisher : World Scientific
Page : 490 pages
File Size : 50,8 Mb
Release : 2022-10-21
Category : Mathematics
ISBN : 9789811263507
Professor Xihua Cao (1920-2005) was a leading scholar at East China Normal University (ECNU) and a famous algebraist in China. His contribution to the Chinese academic circle is particularly the formation of a world-renowned 'ECNU School' in algebra, covering research areas include algebraic groups, quantum groups, algebraic geometry, Lie algebra, algebraic number theory, representation theory and other hot fields. In January 2020, in order to commemorate Professor Xihua Cao's centenary birthday, East China Normal University held a three-day academic conference. Scholars at home and abroad gave dedications or delivered lectures in the conference. This volume originates from the memorial conference, collecting the dedications of scholars, reminiscences of family members, and 16 academic articles written based on the lectures in the conference, covering a wide range of research hot topics in algebra. The book shows not only scholars' respect and memory for Professor Xihua Cao, but also the research achievements of Chinese scholars at home and abroad.
Author : Grant Walker,Reginald M. W. Wood
Publisher : Cambridge University Press
Page : 371 pages
File Size : 43,9 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781108414487
The first of two volumes covering the Steenrod algebra and its various applications. Suitable as a graduate text.
Author : Grant Walker,Reginald M. W. Wood
Publisher : Cambridge University Press
Page : 381 pages
File Size : 51,8 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9781108414456
The second of two volumes covering the Steenrod algebra and its various applications. Ideal for researchers in pure mathematics.
Author : Chris Godsil,Hanmeng Zhan
Publisher : Cambridge University Press
Page : 151 pages
File Size : 49,8 Mb
Release : 2022-12-31
Category : Computers
ISBN : 9781009261685
Explore the mathematics arising from discrete quantum walks in this introduction to a rapidly developing area.
Author : Peter H. Kropholler,Ian J. Leary,Conchita Martínez-Pérez,Brita E. A. Nucinkis
Publisher : Cambridge University Press
Page : 277 pages
File Size : 49,8 Mb
Release : 2018
Category : Mathematics
ISBN : 9781316623220
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Author : C. T. J. Dodson,George Galanis,Efstathios Vassiliou
Publisher : Cambridge University Press
Page : 315 pages
File Size : 53,8 Mb
Release : 2016
Category : Mathematics
ISBN : 9781316601952
A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.
Author : Aurelian Gheondea
Publisher : Cambridge University Press
Page : 511 pages
File Size : 52,7 Mb
Release : 2022-07-28
Category : Mathematics
ISBN : 9781108969031
Presents a modern, readable introduction to spaces with indefinite inner product and their operator theory.
Author : Vladimir Dotsenko,Sergey Shadrin,Bruno Vallette
Publisher : Cambridge University Press
Page : 187 pages
File Size : 47,5 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781108965644
Covering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Author : Dzmitry Badziahin,Alexander Gorodnik,Norbert Peyerimhoff
Publisher : Cambridge University Press
Page : 341 pages
File Size : 43,7 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781107552371
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.