I am currently working on some generalisations of known results in 2-category theory, and I have been stymied trying to find references that discuss `graded-finite dimensional' algebras over a field - that is, the algebra itself is infinite dimensional over the field, but each component of the grading is a finite-dimensional vector space over the field. The references I have found seem to either focus on finite dimensional algebras or on infinite dimensional Lie algebras. Can anyone recommend any references that cover this area?

Thanks,

James