Linear Algebraic Groups pp 65-78 | Cite as

# Lie Algebras

Chapter

## Abstract

The object of this section is to attach to an algebraic group a Lie algebra (in a suitably functorial way). For our purpose, a **Lie algebra** over K is a subspace of an associative K-algebra which is closed under the **bracket** operation [*x, y*] *= xy − yx.* An important example is the **general linear algebra** gl(*n*, K), which is the associative algebra M(*n*, K) viewed as Lie algebra. (This will turn out to be essentially the Lie algebra of GL(*n*, K).)

## Keywords

Tangent Space Tangent Vector Algebraic Group Closed Subgroup Affine Space
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## Copyright information

© Springer-Verlag New York Inc. 1975