Quantum Linear Groups
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Quantum Linear Groups
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Author : Brian Parshall
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Quantum Linear Groups written by Brian Parshall 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 1991 with Mathematics categories.
We consider the theory of quantum groups as a natural abstraction of the theory of affine group schemes. After establishing the foundational results as the theory of induced representations, rational cohomology, and the Hochschild-Serre spectral sequence, we take up a detailed investigation of the quantum linear group [italic]GL[italic subscript]q([italic]n). In particular, we develop the global and infinitesimal representation theory of [italic]GL[italic subscript]q([italic]n) and its subgroups.
Quantum Linear Groups And Representations Of Gl N Mathbb F Q
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Author : Jonathan Brundan
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Quantum Linear Groups And Representations Of Gl N Mathbb F Q written by Jonathan Brundan 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 2001 with Mathematics categories.
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group.
Quantum Linear Groups
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Author : Brian Parshall
language : en
Publisher:
Release Date : 1991
Quantum Linear Groups written by Brian Parshall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Group schemes categories.
Lie Group Machine Learning
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Author : Fanzhang Li
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
Lie Group Machine Learning written by Fanzhang Li and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Computers categories.
This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.
Quantum Groups
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Author : Vladimir K. Dobrev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-07-10
Quantum Groups written by Vladimir K. Dobrev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-10 with Science categories.
With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies
Representation Theory Of Finite Groups And Finite Dimensional Algebras
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Author : Michler
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Representation Theory Of Finite Groups And Finite Dimensional Algebras written by Michler and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.
Representations Of Algebraic Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Representations Of Algebraic Groups written by Jens Carsten Jantzen 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 2003 with Mathematics categories.
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Global Ic Bases For Quantum Linear Groups
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Author : Jie Du
language : en
Publisher:
Release Date : 1994
Global Ic Bases For Quantum Linear Groups written by Jie Du and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebras, Linear categories.
Group Theory In China
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Author : Zhexian Wan
language : en
Publisher: Springer Science & Business Media
Release Date : 1996
Group Theory In China written by Zhexian Wan 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 1996 with Mathematics categories.
Hsio-Fu Tuan is a Chinese mathematician who has made important contributions to the theories of both finite groups and Lie groups. He has also had a great influence on the development of algebra, and particularly group theory in China. The present volume consists of a collection of essays on various aspects of group theory written by some of his former students and colleagues in honour of his 80th birthday. The papers contain the main general results, as well as recent ones, on certain topics within this discipline. The chief editor, Zhe-Xian Wan, is a leading algebraist in China.
Noncommutative Geometry And Quantum Groups
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Author : Piotr M. Hajac
language : en
Publisher:
Release Date : 2003
Noncommutative Geometry And Quantum Groups written by Piotr M. Hajac and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Geometry, Algebraic categories.