When has the exterior algebra A (viewed just as an algebra, not considered as a graded algebra) of an $n$-dimensional vector space over a field $K$ the structure of a Hopf algebra? (depending on n and K) When is it a symmetric algebra? (I know how to check when it is symmetric, but is there a reference?) Possibly harder question: Is there a finite dimensional, nonprojective module M over A with $Ext^{1}(M,M)=0$? Can one classify all periodic modules over this algebra? (posted here: http://math.stackexchange.com/questions/2015144/when-is-the-exterior-algebra-a-hopf-algebra )