Towards Gauge theory for a class of commutative and non-associative fuzzy spaces

Abstract

We discuss gauge theories for commutative but non-associative algebras related to the $ SO(2k+1)$ covariant finite dimensional fuzzy $2k$-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to be generalized to be functions of coordinates as well as derivatives. The usual gauge fields depending on coordinates only are recovered after a partial gauge fixing.The deformation parameter for these commutative but non-associative algebras is a scalar of the rotation group. This suggests interesting string-inspired algebraic deformations of spacetime which preserve Lorentz-invariance.