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Ausland-Reiten Quiver - knitting

Given a quiver representation

 A3= DiGraph({1:{2:['a']}, 2:{3:['b']}})

or

 A4= DiGraph({1:{2:['a']}, 2:{3:['b']}, 3:{4:['b']}})

do you know a script or an algorithm which can be downloaded or is part of a library to perform knitting for determining the Auslander-Reiten quiver, for simple cases such as above. The above are the Dynkin diagrams of type A3 and A4. Knitting is described in A. Schiffler, Quiver Representations, Springer, 2014, p. 70 f. I realize there is a way to calculate the Auslander-Reiten-Translate (https://doc.sagemath.org/html/en/reference/quivers/sage/quivers/representation.html).

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updated 1 year ago

dan_fulea gravatar image

Ausland-Reiten Quiver - knitting

Given a quiver representation

 A3= DiGraph({1:{2:['a']}, 2:{3:['b']}})
A3 = DiGraph({1 : {2 : ['a']}, 
               2 : {3 : ['b']}})

or

 A4= DiGraph({1:{2:['a']}, 2:{3:['b']}, 3:{4:['b']}})
A4 = DiGraph({1 : {2 : ['a']}, 
               2 : {3 : ['b']},
               3 : {4 : ['b']}})

do you know a script or an algorithm which can be downloaded or is part of a library to perform knitting for determining the Auslander-Reiten quiver, for simple cases such as above. The above are the Dynkin diagrams of type A3 A3 and A4. A4.

Knitting is described in A. Schiffler, Quiver Representations, Springer, 2014, p. 70 f. I realize there is a way to calculate the Auslander-Reiten-Translate (https://doc.sagemath.org/html/en/reference/quivers/sage/quivers/representation.html). (https://doc.sagemath.org/html/en/reference/quivers/sage/quivers/representation.html).

click to hide/show revision 3
None

updated 1 year ago

FrédéricC gravatar image

Ausland-Reiten Quiver - knitting

Given a quiver representation

 A3 = DiGraph({1 : {2 : ['a']}, 
               2 : {3 : ['b']}})

or

 A4 = DiGraph({1 : {2 : ['a']}, 
               2 : {3 : ['b']},
               3 : {4 : ['b']}})

do you know a script or an algorithm which can be downloaded or is part of a library to perform knitting for determining the Auslander-Reiten quiver, for simple cases such as above. The above are the Dynkin diagrams of type A3 and A4.

Knitting is described in A. Schiffler, Quiver Representations, Springer, 2014, p. 70 f. I realize there is a way to calculate the Auslander-Reiten-Translate (https://doc.sagemath.org/html/en/reference/quivers/sage/quivers/representation.html).