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March 2012 Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces
Hironao Kato
Hiroshima Math. J. 42(1): 1-35 (March 2012). DOI: 10.32917/hmj/1333113005

Abstract

We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups admitting irreducible left invariant flat complex projective structures. As a result, direct sums of special linear Lie algebras $\sll(2) \oplus \sll(m_1) \oplus \cdots \oplus \sll(m_k)$ admit left invariant flat complex projective structures if the equality $4 + m_1^2 + \cdots + m_k^2 -k - 4 m_1 m_2 \cdots m_k = 0$ holds. These contain $\sll(2)$, $\sll(2) \oplus \sll(3)$, $\sll(2) \oplus \sll(3) \oplus \sll(11)$ for example.

Citation

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Hironao Kato. "Left invariant flat projective structures on Lie groups and prehomogeneous vector spaces." Hiroshima Math. J. 42 (1) 1 - 35, March 2012. https://doi.org/10.32917/hmj/1333113005

Information

Published: March 2012
First available in Project Euclid: 30 March 2012

zbMATH: 1294.53018
MathSciNet: MR2952071
Digital Object Identifier: 10.32917/hmj/1333113005

Subjects:
Primary: 11S90, 53B1
Secondary: 53C10

Rights: Copyright © 2012 Hiroshima University, Mathematics Program

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Vol.42 • No. 1 • March 2012
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