This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups, and the finite dimensional Hopf algebras over fields are exhibited. This volume is self contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.
This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.
This is the first of two volumes which will provide a comprehensive introduction to the modern representation theory of Frobenius algebras. The first part of the book serves as a general introduction to basic results and techniques of the modern representation theory of finite dimensional associative algebras over fields, including the Morita theory of equivalences and dualities and the Auslander-Reiten theory of irreducible morphisms and almost split sequences. The second part is devoted to fundamental classical and recent results concerning the Frobenius algebras and their module categories. Moreover, the prominent classes of Frobenius algebras, the Hecke algebras of Coxeter groups, and the finite dimensional Hopf algebras over fields are exhibited. This volume is self contained and the only prerequisite is a basic knowledge of linear algebra. It includes complete proofs of all results presented and provides a rich supply of examples and exercises. The text is primarily addressed to graduate students starting research in the representation theory of algebras as well as mathematicians working in other fields.
This volume contains 20 papers presented at the Sixth International Nobeyama Workshop on the New Century of Computational Fluid Dynamics, Nobeyama, Japan, April 21-24, 2003. The Nobeyama Workshop focuses on predicting the next one hundred years of development of Fluid Dynamics, accounting for the current status and future trends of high performance computation and communication. The papers cover computational electromagnetics, astrophysical topics, CFD research and applications in general, large-eddy simulation, vortical flows, mesh generation topics, visualization, DNA computing, multidisciplinary simulation and optimisation, as well as algorithmic developments. The Workshops are known for the informal and concentrated atmosphere of in-depth discussion thanks to all the efforts of Prof. Kunio Kuwahara at ISAS, Japan. In celebration of his 60th birthday, this workshop was dedicated to him.
Monograph on the trend towards workers participation in Japan - examines changes in management attitudes and employees attitudes in response to technological change, and includes survey data on workers' motivation, job satisfaction and leisure activities, etc. Bibliography pp. 215 to 221 and statistical tables.
Showing the relation of physics to circuit interruption technology, describes for engineers the switching phenomena, test procedures, and applications of modern, high-voltage circuit breakers, especially SF, gas-blast, and the vacuum types used in medium-voltage ranges. Applies the physical arc mode
This is a photographic exploration of the characteristic colours of Japan that have appeared repeatedly throughout the centuries in everything from everyday utensils to works of high art. The Colors of Japan is a visually stunning look into the unique use of color in Japanese culture from prehistoric times to the present day. That the Japanese should possess their own sense of color is not surprising, for like almost every other aspect of human life, color perception varies from culture to culture. The first and most fundamental reason for this variation can be
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