Abstract
Free field equations, with various spins, for space–time algebras with second-rank tensor (instead of the usual vector) momentum are constructed. Similar algebras are appearing in superstring/M theories. Special attention is paid to gauge invariance properties, in particular the spin-two equations with gauge invariance are constructed for dimensions 2+2 and 2+4, and the connection with Einstein equation and diffeomorphism invariance is established.
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