## The structure of non-commutative deformation

Hello, I am a Ph.D student in Poisson geometry. My thesis is based on the work by E. Hawkins [link text] "The structure of non-commutative deformation". In page 22, Hawkins defines a connection $\nabla$, which I really can't hunderstand how it is defined. So my questions are the following:

1. How is $\nabla$ defined ?
2. What does "$A^a_{\alpha}$ is the potentiel for $\nabla$" mean ?
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 I'd suggest that you put a little more effort into asking your question. Why don't you put the definition you are asking about into the question? – MTS Jan 15 2012 at 20:03