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April 2019 Reduced contragredient Lie algebras and PC Lie algebras
Nagatoshi Sasano
Osaka J. Math. 56(2): 289-299 (April 2019).


Using the theory of standard pentads, we can embed an arbitrary finite-dimensional reductive Lie algebra and its finite-dimensional completely reducible representation into some larger graded Lie algebra. However, it is not easy to find the structure of the ``larger graded Lie algebra'' from the definition in general cases. Under these, the first aim of this paper is to show that the ``larger graded Lie algebra'' is isomorphic to some PC Lie algebra, which are Lie algebras corresponding to special standard pentads called pentads of Cartan type. The second aim is to find the structure of a PC Lie algebra.


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Nagatoshi Sasano. "Reduced contragredient Lie algebras and PC Lie algebras." Osaka J. Math. 56 (2) 289 - 299, April 2019.


Published: April 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07080086
MathSciNet: MR3934977

Primary: 17B65
Secondary: 17B67, 17B70

Rights: Copyright © 2019 Osaka University and Osaka City University, Departments of Mathematics


Vol.56 • No. 2 • April 2019
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