Revision history [back]

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 $\mathbb{A}_3$ and $\mathbb{A}_4$. 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).

 2 None dan_fulea 5397 ●5 ●43 ●91

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 $\mathbb{A}_3$ $\Bbb A_3$ and $\mathbb{A}_4$. $\Bbb A_4$.

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).

 3 None FrédéricC 5141 ●3 ●43 ●112

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 $\Bbb A_3$ and $\Bbb A_4$.

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).