• Corpus ID: 231662409

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… 

References

SHOWING 1-10 OF 20 REFERENCES

Current Algebras and Groups

Let M be a smooth manifold and G a Lie group. In this book we shall study infinite-dimensional Lie algebras associated both to the group Map(M, G) of smooth mappings from M to G and to the group of

Loop groups

In these notes, we introduce matrix Lie groups G and their Lie algebras Lie(G), and we exhibit the (continuous) loop group LG as a smooth Banach Lie group. Prerequisites are basic calculus and point

Dirac Operators in Riemannian Geometry

Clifford algebras and spin representation Spin structures Dirac operators Analytical properties of Dirac operators Eigenvalue estimates for the Dirac operator and twistor spinors Seiberg-Witten

Clifford Algebras and Dirac Operators in Harmonic Analysis

1. Clifford algebras 2. Dirac operators and Clifford analyticity 3. Dirac operators and the spin group 4. Dirac operators in the analysis on Euclidean space 5. Dirac operators in representation

Introduction to Lie Algebras and Representation Theory

Preface.- Basic Concepts.- Semisimple Lie Algebras.- Root Systems.- Isomorphism and Conjugacy Theorems.- Existence Theorem.- Representation Theory.- Chevalley Algebras and Groups.- References.-

Lie algebra of the infinitesimal automorphisms on $S^3$ and its central extension

Virasoro algebra is the central extension associated with this two cocycle. A highest w eight representation o f the V iraso ro a lgeb ra is genera ted by a h ighest w e igh t rep resen ta tion o f t