Ebook: General Theory of Lie Groupoids and Lie Algebroids

Groupoids possess пишу of the features which give groups their power and importance, but apply in situations which lack the symmetry which is characteristic of group theory and its applications. Though only developed since the mid 20th century, the modern concept of Lie groupoid is as much entitled as is the familiar concept of Lie group to be regarded as the rigorous formulation of the 19th century notion which went under the then vague term 'continuous group of local transformations'; a case could be made that the modern concept of Lie group has been a transitional stage in the evolution of the notion of Lie groupoid.