The three letters "PBW" are commonly used as an adjective in algebra, combinatorics, and representation theory, but to indicate what? Is there a difference between a "PBW algebra" and a "PBW deformation"? Do all thing of "PBW-type" exhibit a "PBW property"? And who gets the credit for proving the original PBW-theorem anyway, Poincare or Birkhoff or Witt? We sample various notions of PBW-ness in the literature.
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