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
- Mathematics
- 1989
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
- Mathematics
- 2016
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
- Mathematics
- 2000
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
- Mathematics
- 1991
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…
Clifford Algebra and Spinor-Valued Functions: A Function Theory For The Dirac Operator
- Mathematics
- 2012
Introduction to Lie Algebras and Representation Theory
- Mathematics
- 1973
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
- Mathematics
- 1996
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…