# Current algebras on S^3 of complex Lie algebras

@inproceedings{Kori2021CurrentAO, title={Current algebras on S^3 of complex Lie algebras}, author={Tosiaki Kori}, year={2021} }

Let L be the space of spinors on S3 that are the restrictions to S3 of the Laurent polynomial type harmonic spinors on C2. L becomes an associative algebra. For a simple Lie algebra g the real Lie algebra Lg generated by L⊗C g is called g-current algebra. The real part K of L becomes a commutative subalgebra of L. For the Cartan subalgebra h of g , Kh = K ⊗R h becomes a Cartan subalgebra of Lg. We investigate the adjoint representation of Kh and find that the set of non-zero weights corresponds…

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