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Supergravity by Daniel Z. Freedman, Antoine Van Proeyen

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Lie groups, Lie algebras, and superalgebras play an important role in supergravity. In this appendix we review the basic ideas with a focus on the classification of these objects. There are many textbooks available for readers who desire more information.

B.1   Groupsandrepresentations

All groups have composition laws. If g1 and g2 are any two elements, then their product g1g2 = g3 where g3 is a third element. We consider continuous groups (Lie groups) here. This means that the gi are functions of parameters that vary continuously. The dimension of the group is the number of parameters. The most important groups are the classical groups

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