6533b7defe1ef96bd12764de

RESEARCH PRODUCT

The Virasoro Algebra

Jouko Mickelsson

subject

Filtered algebraHigh Energy Physics::TheoryPure mathematicsMathematics::Quantum AlgebraCurrent algebraCellular algebraVirasoro algebraUniversal enveloping algebraWitt algebraAffine Lie algebraMathematicsSupersymmetry algebra

description

In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representation theory of the algebra of vector fields on a higher dimensional manifold is much less understood; we shall discuss the extensions of these algebras in Section 7.6.

yearjournalcountryeditionlanguage
1989-01-01
https://doi.org/10.1007/978-1-4757-0295-8_7