C N Pope and L J Romans 1990 Class. Quantum Grav. 7 97 doi:10.1088/0264-9381/7/1/015
C N Pope and L J Romans
Show affiliationsThe authors show that recent approaches investigating the infinite-dimensional algebras of area-preserving diffeomorphisms for the sphere and the torus in the context of membrane theory may be extended to non-orientable manifolds. They show that the analogous algebra for the Klein bottle is obtainable as an n to infinity limit of SO(2n) algebras, and display a central extension for the algebra. For the real projective plane, they give three different constructions of the algebra, as limits of algebras of the form SO(2n-1)*SO (2n+1), USp(2n)*USp(2n+2) and USp(2n). They also show that the area-preserving algebra for the torus can be described as the limit of finite-dimensional algebras of many different forms, of which SU(n) is just one example.
02.20.Qs General properties, structure, and representation of Lie groups
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
17B45 Lie algebras of linear algebraic groups (See also 14Lxx and 20Gxx)
Issue 1 (January 1990)
C N Pope and L J Romans 1990 Class. Quantum Grav. 7 97
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