Finite Dimensional Algebras and Related Topics

Author: V. Dlab,Leonard Scott

Publisher: Springer Science & Business Media

ISBN: 9401715564

Category: Mathematics

Page: 392

View: 9935

Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Finite Dimensional Algebras

Author: Yurj A. Drozd,Vladimir V. Kirichenko

Publisher: Springer Science & Business Media

ISBN: 3642762441

Category: Mathematics

Page: 249

View: 4117

This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.

Representations of Finite-Dimensional Algebras

Author: Peter Gabriel,Andrei V. Roiter

Publisher: Springer Science & Business Media

ISBN: 9783540629900

Category: Mathematics

Page: 177

View: 6382

From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette

Finite Dimensional Algebras and Quantum Groups

Author: Bangming Deng,Jie Du,Brian Parshall

Publisher: American Mathematical Soc.

ISBN: 0821841866

Category: Mathematics

Page: 759

View: 2007

This book represents the first treatment in book form of both finite dimensional algebras and quantum groups, offering comprehensive coverage of the two theories given in its title. It emphasizes the finite dimensional algebra approach to quantum groups. This modern treatment includes a great depth of coverage of more recent results.

Representations of Finite Dimensional Algebras

Proceedings of the Tsukuba International Conference (fifth ICRA) Held August 13-18, 1990

Author: Hiroyuki Tachikawa,Vlastimil Dlab,Canadian Mathematical Society

Publisher: American Mathematical Soc.

ISBN: 9780821860168

Category: Mathematics

Page: 322

View: 2577

This volume contains the proceedings of the Tsukuba International Conference on Representations of Algebras and Related Topics (fifth ICRA), held at the University of Tsukuba, August 13-18, 1990. The conference focused on the rapid development of research on representations of finite-dimensional algebras and group representations. A subset of the fifty-seven lectures are collected here, together with a number of other papers not originally presented at the conference. With contributions by some of the world's leading experts in this area, this book provides a valuable overview of the frontier of research in representations of algebras.

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Author: Vlastimil Dlab,Claus Michael Ringel

Publisher: American Mathematical Soc.

ISBN: 0821834169

Category: Mathematics

Page: 479

View: 7726

These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional 'instructional' workshop preceding the conference, there were also workshops on 'Commutative Algebra, Algebraic Geometry and Representation Theory', 'Finite Dimensional Algebras, Algebraic Groups and Lie Theory', and 'Quantum Groups and Hall Algebras'. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated.The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented.The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.

Representation Theory of Finite Groups and Finite-Dimensional Algebras

Proceedings of the Conference at the University of Bielefeld from May 15–17, 1991, and 7 Survey Articles on Topics of Representation Theory

Author: Michler,Ringel

Publisher: Birkhäuser

ISBN: 3034886586

Category: Mathematics

Page: 522

View: 7704

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.

Trends in the Representation Theory of Finite Dimensional Algebras

1997 Joint Summer Research Conference on Trends in the Representation Theory of Finite Dimensional Algebras, July 20-24, 1997, Seattle, Washington

Author: Edward L. Green,Birge Huisgen-Zimmermann

Publisher: American Mathematical Soc.

ISBN: 0821809288

Category: Mathematics

Page: 356

View: 957

This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory. It's features include: work outlining significant progress on long-standing open problems; survey articles offering both overviews and introductions to various subfields of the topic; and, expositions reflecting the interplay between the representation theory of algebras and other fields.

Finite Dimensional Algebras and Quantum Groups

Author: N.A

Publisher: American Mathematical Soc.

ISBN: 9780821875315

Category: Mathematics

Page: 759

View: 8247

"The interplay between finite dimensional algebras and Lie theory dates back many years. In more recent times, these interrelations have become even more strikingly apparent. This text combines, for the first time in book form, the theories of finite dimensional algebras and quantum groups. More precisely, it investigates the Ringel-Hall algebra realization for the positive part of a quantum enveloping algebra associated with a symmetrizable Cartan matrix and it looks closely at the Beilinson-Lusztig-MacPherson realization for the entire quantum $\mathfrak{gl}_n$. The book begins with the two realizations of generalized Cartan matrices, namely, the graph realization and the root datum realization. From there, it develops the representation theory of quivers with automorphisms and the theory of quantum enveloping algebras associated with Kac-Moody Lie algebras. These two independent theories eventually meet in Part 4, under the umbrella of Ringel-Hall algebras. Cartan matrices can also be used to define an important class of groups--Coxeter groups--and their associated Hecke algebras. Hecke algebras associated with symmetric groups give rise to an interesting class of quasi-hereditary algebras, the quantum Schur algebras. The structure of these finite dimensional algebras is used in Part 5 to build the entire quantum $\mathfrak{gl}_n$ through a completion process of a limit algebra (the Beilinson-Lusztig-MacPherson algebra). The book is suitable for advanced graduate students. Each chapter concludes with a series of exercises, ranging from the routine to sketches of proofs of recent results from the current literature."--Publisher's website.

Trends in the Representation Theory of Finite Dimensional Algebras

1997 Joint Summer Research Conference on Trends in the Representation Theory of Finite Dimensional Algebras, July 20-24, 1997, Seattle, Washington

Author: Joint Summer Research Conference on Trends in the Representation theor,Edward L. Green,Birge Huisgen-Zimmermann

Publisher: The National Academies

ISBN: 9780821809280

Category: Mathematics

Page: 356

View: 2871

This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory. It's features include: work outlining significant progress on long-standing open problems; survey articles offering both overviews and introductions to various subfields of the topic; and, expositions reflecting the interplay between the representation theory of algebras and other fields.

Finite-Dimensional Division Algebras Over Fields

Author: Nathan Jacobson

Publisher: Springer Science & Business Media

ISBN: 9783540570295

Category: Mathematics

Page: 278

View: 3903

Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).

Finite Dimensional Algebras and Quantum Groups

Author: Bangming Deng,Jie Du,Brian Parshall

Publisher: American Mathematical Soc.

ISBN: 0821841866

Category: Mathematics

Page: 759

View: 2927

This book represents the first treatment in book form of both finite dimensional algebras and quantum groups, offering comprehensive coverage of the two theories given in its title. It emphasizes the finite dimensional algebra approach to quantum groups. This modern treatment includes a great depth of coverage of more recent results.

Representations of Algebras

Author: Fla'vio Ulhoa Coelho,Hector Goldschimdt

Publisher: CRC Press

ISBN: 9780824707330

Category: Mathematics

Page: 306

View: 4050

This volume contains the proceedings of the Conference on Representations of Algebras - Sao Paulo (CRASP), held at the Instituto de Matematica e Estatistica of the Universidade de Sao Paulo, Brazil. It discusses Hopf, tubular, quasischurian, wild hereditary, concealed-canonical Artin, Brauer star, and Koszul algebras.