Can class recall be considered as class accuracy?

I find the notion of accuracy-per-class very interesting but I don't find any known metrics for it in the literature.

I was thinking, can we consider that, in a multi-class classification problem, the recall of a given class represents the accuracy of our model regarding this class? because basically the recall of a given class represents the proportion of items well classified from that class, right? And this is what accuracy is about. If not, is there a metric for accuracy-per-class that I am missing?

Ps: When I say the class recall, I am refering to the recall computed by sklearn classification_report for each label of the multi-class classification problem: recall = TP/(TP+FN)

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