ordinary quiver of an algebra
Let be a field and an algebra over .
Denote by the (Jacobson) radical of and a square of radical.
Definition. The ordinary quiver of a finite-dimensional algebra is defined as follows:
The set of vertices is equal to which is in bijective correspondence with .
If , then the number of arrows from to is equal to the dimension of the -vector space
It can be shown that the ordinary quiver is well-defined, i.e. it is independent on the choice of a complete set of primitve orthogonal idempotents. Also finite dimension of implies, then the ordinary quiver is finite.
|Title||ordinary quiver of an algebra|
|Date of creation||2013-03-22 19:17:41|
|Last modified on||2013-03-22 19:17:41|
|Last modified by||joking (16130)|