Table Of Lie Groups

We remark on the Topological properties of the group ( Dimension , Connectedness , Compactness , the nature of the Fundamental Group , and whether or not they are Simply Connected ), as well as on their algebraic properties ( Abelian , Simple , Semisimple ).

For more examples of Lie groups and other related topics see the List Of Simple Lie Groups and the List Of Lie Group Topics .

REAL LIE GROUPS AND THEIR ALGEBRAS

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CM: Is this group ''G'' Compact ? (Yes or No)

$\pi_0$ : Gives the Group Of Components of ''G''. The order of the component group gives the number of Connected Components . The group is Connected iff the component group is Trivial (denoted by 0).

$\pi_1$ : Gives the Fundamental Group of ''G'' whenever ''G'' is connected. The group is Simply Connected iff the fundamental group is Trivial (denoted by 0).

UC: If ''G'' is not simply connected, gives the Universal Cover of ''G''.

REAL LIE ALGEBRAS

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S: Is this algebra simple? (Yes or No)

SS: Is this algebra Semi-simple ? (Yes or No)

COMPLEX LIE GROUPS AND THEIR ALGEBRAS

The dimensions given are dimensions over C. Note that every complex Lie group/algebra can also be viewed as a real Lie group/algebra of twice the dimension.

COMPLEX LIE ALGEBRAS

The dimensions given are dimensions over C. Note that every complex Lie algebra can also be viewed as a real Lie algebra of twice the dimension.

REFERENCES

William Fulton and Joe Harris, ''Representation Theory, A First Course'' (1991) Springer Verlag New York, ISBN 0-387-974495-4.

	CATEGORIES ABOUT TABLE OF LIE GROUPS

	lie groups

	lie algebras

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Table Of Lie Groups