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--- advanced_tools:group_theory:lie_algebras [2018/04/08 12:13]
jakobadmin [Abstract]
+++ advanced_tools:group_theory:lie_algebras [2023/03/29 17:40]
132.76.61.54 fur -> for
@@ Line 4: / Line 4: @@
 <tabbox Intuitive>
 The Lie algebras consist of infinitesimally small transformations and are used in physics to describe [[basic_tools:symmetry|symmetries]]. Since arbitrarily large continuous transformations can be built up from tiny ones, almost everything that is important about continuous transformations is encoded in the infinitesimal ones.
+Formulated differently, Lie algebras describe infinitesimal symmetries.
@@ Line 48: / Line 50: @@
 ** Definition:**
-<WRAP tip> For a matrix Lie group $G$ the corresponding Lie algebra  $\mathfrak{g}$ can be defined as the set of matrices $X$ that yield $e^{tX} \in G$ für $t \in \mathbb{R}$.</WRAP>
+<WRAP tip> For a matrix Lie group $G$ the corresponding Lie algebra  $\mathfrak{g}$ can be defined as the set of matrices $X$ that yield $e^{tX} \in G$ for $t \in \mathbb{R}$.</WRAP>
 **The Natural Product of a Lie Algebra:**