2022-02-20

32: General Linear Lie Algebra, \mathfrak{gl} (V)

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A definition of general linear Lie algebra, \(\mathfrak{gl} (V)\)

Topics


About: Lie algebra

The table of contents of this article


Starting Context



Target Context


  • The reader will have a definition of general linear Lie algebra, \(\mathfrak{gl} (V)\).

Orientation


There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.


Main Body


1: Definition


For any vectors space, \(V\), the Lie algebra whose elements are all the vectors space endomorphisms on \(V\) with the canonical vectors space structure (scalar multiplication and addition are possible, because the codomain is a vectors space) and bracket as the commutator of the argument endomorphisms, which means that \([f_1, f_2] = f_1 \circ f_2 - f_2 \circ f_1\)


References


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