UC San Diego

We construct three examples of affine, associative algebras with relatively low growth. We construct an algebra over an arbitrary countable field that is affine, infinite dimensional, nil, N-graded, and has Gelfand- Kirillov dimension at most 3. We construct an algebra over an arbitrary field that is affine, infinite dimensional, nil, N-graded, and whose growth can be asymptotically bounded above by an arbitrary non-polynomial function. We construct an algebra over an arbitrary, algebraically closed field that is affine, infinite dimensional, N- graded, Jacobson radical, and has quadratic growth