# Rank of a Lie group

From Encyclopedia of Mathematics

*(real or complex)*

The (real, respectively, complex) dimension of any Cartan subgroup of it. The rank of a Lie group coincides with the rank of its Lie algebra (see Rank of a Lie algebra). If a Lie group $G$ coincides with the set of real or complex points of a linear algebraic group $\widehat G$, then the rank of $G$ coincides with the rank of $\widehat G$ (cf. Rank of an algebraic group).

#### References

[a1] | R.W. Carter, "Simple groups of Lie type" , Wiley (Interscience) (1972) Chapt. 1 ISBN 0-471-13735-9 |

[a2] | V.S. Varadarajan, "Lie groups, Lie algebras, and their representations" , Prentice-Hall (1974) MR0376938 Zbl 0371.22001 |

[a3] | A.W. Knapp, "Representation theory of semisimple groups" , Princeton Univ. Press (1986) MR0855239 Zbl 0604.22001 |

[a4] | J.E. Humphreys, "Linear algebraic groups" , Springer (1975) pp. Sect. 35.1 MR0396773 Zbl 0325.20039 |

**How to Cite This Entry:**

Rank of a Lie group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Rank_of_a_Lie_group&oldid=55784

This article was adapted from an original article by V.L. Popov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article