On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasi-conformal infinite-dimensional algebras AC(so(4, 1)) and PAC(so(3, 2)) extending the conformal algebras in three-dimensional euclidean and Minkowski space-time like the Virasoro algebra extends so(2, 1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D > 2 and possible applications in exactly solvable conformal quantum field models in D > 2 are discussed.
ASJC Scopus subject areas
- Nuclear and High Energy Physics