nLab
group theory

Contents

Context

Mathematics

Group Theory

Contents

Idea

The study of groups.

There are many generalizations and related structures; for example the vertical categorifications of groups like 2-groups, horizontal categorifications as groupoids, groups with structure, like topological groups, Lie groups, thus also Lie groupoids, Lie infinity-groupoids; and noncommutative generalizations like quantum groups. Lie and algebraic group(oid)s have their infinitesimal precursors like formal groups, local Lie groups, tangent Lie algebras, tangent Lie algebroids etc. In the smooth context the relation between Lie groupoids and Lie algebroids is the subject of Lie theory.

Literature

Textbook accounts

in relation to applications in physics:

See also:

category: group theory

Last revised on September 16, 2021 at 07:23:23. See the history of this page for a list of all contributions to it.