Abstract
We extend the statement of Melville theorem about smallness of centroids of invariant nilpotent subalgebras of semi-simple complex Lie algebras to the whole class of invariant subalgebras of reductive Lie algebras over any field of zero characteristic.
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References
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K.N. Ponomarev. (1998) Fields of representatives of commutative local rings and maximal scalar fields of finite-dimensional algebras. Algebra and logic. 37, 380–390.
D.J. Melville. (1992) Centroids of nilpotent Lie algebras. Comm.in algebra, 20, 3649–3682.
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Ponomarev, K.N. (2004). Some Generalization of Melville Theorem. In: Christensen, C., Sathaye, A., Sundaram, G., Bajaj, C. (eds) Algebra, Arithmetic and Geometry with Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18487-1_39
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DOI: https://doi.org/10.1007/978-3-642-18487-1_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00475-2
Online ISBN: 978-3-642-18487-1
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