This book provides an elementary introduction to the theory of groupoids and their representations, encompassing the standard theory of groups with plenty of examples and applications ranging from combinatorics to the topology of graphs.
This book provides an elementary introduction to the theory of groupoids and their representations, encompassing the standard theory of groups with plenty of examples and applications ranging from combinatorics to the topology of graphs.
Alberto Ibort is full professor of Applied Mathematics in the Department of Mathematics of the Universidad Carlos III of Madrid, Spain and member of the Mathematical Institute, ICMAT, Madrid, Spain. He has been visiting professor and Fulbright Scholar at the University of California at Berkeley, USA, postdoc at the Université de Paris VI, France and the Niels Bohr Institute, Denmark, and professor of Theoretical Physics at the Universidad Complutense of Madrid. His research includes several areas of Mathematics and Mathematical Physics: Functional Analysis, Differential Geometry and more recently algebraic structures on Physics and Engineering, mainly control theory. Miguel A. Rodríguez is full professor in the Department of Theoretical Physics of Universidad Complutense of Madrid, Spain. His teaching is mainly related to courses on Mathematics applied to Physics, in particular group theory. He has been visiting professor at Université de Montréal, Canada, University of California at Los Angeles, USA, and Università di Roma Tre, Italy. His research field includes several areas of Mathematical Physics: Integrable Systems, Group Theory, and Difference Equations.
Inhaltsangabe
1. Categories: basic notions and examples. 2. Groups. 3. Groupoids. 4. Actions of groups and groupoids. 5. Functors and transformations. 6. The structure of groupoids. 7. Linear representations of groups. 8. Characters. 9. Linear representations of categories. 10. Algebras and groupoids. 11. Semi-simplicity. 12. Representations of groupoids. A. Glossary of Linear Algebra. B. Generators and relations. C. Schwinger Algebra. Bibliography. Index.
1. Categories: basic notions and examples. 2. Groups. 3. Groupoids. 4. Actions of groups and groupoids. 5. Functors and transformations. 6. The structure of groupoids. 7. Linear representations of groups. 8. Characters. 9. Linear representations of categories. 10. Algebras and groupoids. 11. Semi-simplicity. 12. Representations of groupoids. A. Glossary of Linear Algebra. B. Generators and relations. C. Schwinger Algebra. Bibliography. Index.
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