A vertex operator algebra is a 
-graded vector space 
with finite-dimensional
homogeneous pieces and 
for sufficiently negative 
with a vacuum, a conformal vector, and a state-field correspondence
satisfying the vacuum, translation, and Jacobi identities.
For a state 
,
its field is the formal series of linear operators
 |
For each 
,
lower truncation means 
, the space of vector-valued formal
Laurent series. The conformal vector supplies the grading operator 
and Virasoro algebra
relations. CFT type means 
with 
, where 
is the vacuum.
