Abstract
We will be interested in complex representations of both real and complex Lie algebras. There is an important distinction to be made. If g is a real Lie algebra, then a complex representation is an ℝ-linear homomorphism g → End(V), where V is a complex vector space. On the other hand, if g is a complex Lie algebra, we require that the homomorphism be (ℂ-linear. The reader should note that we ask more of a complex representation of a complex Lie algebra than we do of a complex representation of a real Lie algebra.
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© 2004 Springer Science+Business Media New York
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Bump, D. (2004). Extension of Scalars. In: Lie Groups. Graduate Texts in Mathematics, vol 225. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4094-3_11
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DOI: https://doi.org/10.1007/978-1-4757-4094-3_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1937-3
Online ISBN: 978-1-4757-4094-3
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