I would object too, but I don't see how that could be confusing moreso than any whiteboard "you get what I mean" pseudocode.

The reader's walking in with knowledge of the product-based construction of N-dimensional space, and we readily admit that "R^2" is (a set literally, but) taken to mean the space equipped with whatever operations appropriate for whatever algebra.

I'm being kinda sophist on this. "G^2" isn't meaningful. I agree. But given the convention of naming a set with the implication of whatever topology/metric/norm, the notation is already under harsh torture, right..?

In my reply to contravariant, I explain why I don't think R^2 constitutes abuse of notation: https://news.ycombinator.com/item?id=13241874 .