⊕_{k≥0} V^{⊗k}, the free associative algebra on V. Universal: any linear map V → A to an associative algebra A extends uniquely to an algebra map T(V) → A.
⊕_{k≥0} V^{⊗k}, the free associative algebra on V. Universal: any linear map V → A to an associative algebra A extends uniquely to an algebra map T(V) → A.