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?



  • $\begingroup$ You might have more luck if you search for terms like "locally finite" or "locally finite-dimensional" rather than "graded-finite" (which isn't a term I would recognise). There are many examples of such algebras, such as polynomial algebras or (quantised or ordinary) enveloping algebras of Lie algebras. You might also want to look for references discussing PBW bases. $\endgroup$ Jul 17, 2017 at 12:26
  • $\begingroup$ Thank you for that @JanGrabowski - I'd used 'locally x' to refer to a relaxing from finitely many objects to infinitely many, so that terminology hadn't occurred to me. Searching 'locally finite-dimensional' is definitely bringing up some results, although I note that some authors use 'locally finite' to mean 'finitely generated subalgebra implies finite dimensional', which is definitely not what I'm looking for. $\endgroup$ Jul 20, 2017 at 9:22


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