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

<The previous article in this series | The table of contents of this series | The next article in this series>

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
• Orientation
• Main Body
• 1: Definition

---

Starting Context

• The reader knows a definition of Lie algebra.
• The reader knows a definition of %field name% vectors space.
• The reader knows a definition of %structure kind name% endomorphism.

---

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

<The previous article in this series | The table of contents of this series | The next article in this series>