Smith and Van den Bergh worked with it, and got some lovely results, in this paper. For example, they show that direct summands of polynomial rings have simple rings of differential operators in positive characteristic. This is still open (as far as I know) in characteristic 0.

It's a particularly interesting paper for the connections it makes with representation types.

Smith and Van den Bergh worked with it, and got some lovely results, in this paper.¹ For example, they show that direct summands of polynomial rings have simple rings of differential operators in positive characteristic. This is still open (as far as I know) in characteristic 0.

It's a particularly interesting paper for the connections it makes with representation types.

¹Smith, Karen E.; Van den Bergh, Michel, Simplicity of rings of differential operators in prime characteristic, Proc. Lond. Math. Soc., III. Ser. 75, No. 1, 32-62 (1997). ZBL0948.16019, MR1444312.