Generalized diffeomorphisms are orthogonal automorphisms \( F \) of \(T+T^*\) covering a diffeomorphism \( f \) and preserving the Courant bracket.
We have proved that the group of generalized diffeomorphisms is the semidirect product
$$ \textrm{Diff}(M) \subset \Omega^2_{cl}(M), $$ where the diffeomorphisms \( f \) act by pushforward on \( T + T^* \), and a closed \(2\)-form \(B\) acts as a \( B \)-field: \( X+\xi\mapsto X+\xi+i_X B \). The \( B \)-fields are a new symmetry, not present in classical geometry, and they will play a very important role.
Note that a diffeomorphism and a \(B\)-field do not commute: $$ \exp(B) \circ g_*= g_* \exp(g^*B) .$$
If you look at automorphisms of \(T\) covering a diffeomorphism \( f \) and preserving the Lie bracket, you only get the differential of the diffeomorphisms, so this approach is consistent with the symmetries of classical differential geometry.
We have proved that the group of generalized diffeomorphisms is the semidirect product
$$ \textrm{Diff}(M) \subset \Omega^2_{cl}(M), $$ where the diffeomorphisms \( f \) act by pushforward on \( T + T^* \), and a closed \(2\)-form \(B\) acts as a \( B \)-field: \( X+\xi\mapsto X+\xi+i_X B \). The \( B \)-fields are a new symmetry, not present in classical geometry, and they will play a very important role.
Note that a diffeomorphism and a \(B\)-field do not commute: $$ \exp(B) \circ g_*= g_* \exp(g^*B) .$$
If you look at automorphisms of \(T\) covering a diffeomorphism \( f \) and preserving the Lie bracket, you only get the differential of the diffeomorphisms, so this approach is consistent with the symmetries of classical differential geometry.
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