∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
-Lie groupoids
-Lie groups
-Lie algebroids
-Lie algebras
The classification of simple Lie groups contains four infinite series of “classical” simple Lie groups:
, the special unitary group
, the special orthogonal group
, the symplectic group
, the special orthogonal group
Apart from this there are five exceptional Lie groups.
graphics grabbed from Schwichtenberg
More generally, other matrix Lie groups, such as the general linear group , may be called “classical”.
Glen Bredon, Section 0.2 of: Introduction to compact transformation groups, Academic Press 1972 (ISBN 9780080873596, pdf)
Howard Georgi, §19 in: Lie Algebras In Particle Physics, Westview Press (1999), CRC Press (2019) [doi:10.1201/9780429499210]
with an eye towards application to (the standard model of) particle physics and grand unified theory
Last revised on January 23, 2024 at 18:21:22. See the history of this page for a list of all contributions to it.