We now know what a Lie algebra is and we know they are abstractions of infinitesimal symmetries, which are given by derivations. Today we will see what we can say about associating infinitesimal symmetries to continuous symmetries: that is, given a matrix Lie group , we will describe its associated Lie algebra of infinitesimal elements [...]
Posts Tagged ‘quaternions’
The quaternions and Lie algebras II
Posted in Lie theory, tagged exponentials, quaternions on June 14, 2011 | 1 Comment »
SU(2) and the quaternions
Posted in algebraic topology, group theory, Lie theory, tagged division algebras, quaternions on February 12, 2011 | 4 Comments »
The simplest compact Lie group is the circle . Part of the reason it is so simple to understand is that Euler’s formula gives an extremely nice parameterization of its elements, showing that it can be understood either in terms of the group of elements of norm in (that is, the unitary group ) or [...]
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