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An Introduction to Groups, Groupoids and Their Representations (Paperback)
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An Introduction to Groups, Groupoids and Their Representations (Paperback)
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This book offers an introduction to the theory of groupoids and
their representations encompassing the standard theory of groups.
Using a categorical language, developed from simple examples, the
theory of finite groupoids is shown to knit neatly with that of
groups and their structure as well as that of their representations
is described. The book comprises numerous examples and
applications, including well-known games and puzzles, databases and
physics applications. Key concepts have been presented using only
basic notions so that it can be used both by students and
researchers interested in the subject. Category theory is the
natural language that is being used to develop the theory of
groupoids. However, categorical presentations of mathematical
subjects tend to become highly abstract very fast and out of reach
of many potential users. To avoid this, foundations of the theory,
starting with simple examples, have been developed and used to
study the structure of finite groups and groupoids. The appropriate
language and notions from category theory have been developed for
students of mathematics and theoretical physics. The book presents
the theory on the same level as the ordinary and elementary
theories of finite groups and their representations, and provides a
unified picture of the same. The structure of the algebra of finite
groupoids is analysed, along with the classical theory of
characters of their representations. Unnecessary complications in
the formal presentation of the subject are avoided. The book offers
an introduction to the language of category theory in the concrete
setting of finite sets. It also shows how this perspective provides
a common ground for various problems and applications, ranging from
combinatorics, the topology of graphs, structure of databases and
quantum physics.
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