Complex Lie algebras corresponding to weighted projective lines

Biquaternions Lie Algebra and Complex-Projective Spaces

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Classification of complex simple Lie algebras via projective geometry

Complex simple Lie algebras were classified by Cartan and Killing 100 years ago. Their proof proceeds by reducing the question to a combinatorical problem: the classification of irreducible root systems, and then performing the classification. We present a new proof of the classification via the projective geometry of homogeneous varieties. Our proof is constructive: we build a homogeneous spac...

Classiication of Complex Simple Lie Algebras via Projective Geometry

Lie Algebras and their corresponding linear groups

biquaternions lie algebra and complex-projective spaces

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...