We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a sufficient criterion for a symmetric degeneration. Then a detailed discussion of type A quivers and their (symmetric) representation theory via Auslander-Reiten theory leads to our main theorem which states that the symmetric degeneration order of a symmetric quiver of finite type is induced by the "usual" degeneration order between representations of the underlying quiver.
On degenerations and extensions of symplectic and orthogonal quiver representations / Cerulli Irelli, Giovanni; Boos, Magdalena. - In: ARKIV FÖR MATEMATIK. - ISSN 0004-2080. - 63:(2025), pp. 61-115. [10.4310/ARKIV.2025.v63.n1.a3]
On degenerations and extensions of symplectic and orthogonal quiver representations
Giovanni Cerulli Irelli
;
2025
Abstract
We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a sufficient criterion for a symmetric degeneration. Then a detailed discussion of type A quivers and their (symmetric) representation theory via Auslander-Reiten theory leads to our main theorem which states that the symmetric degeneration order of a symmetric quiver of finite type is induced by the "usual" degeneration order between representations of the underlying quiver.| File | Dimensione | Formato | |
|---|---|---|---|
|
Cerulli_degenerations_2025.pdf
accesso aperto
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Creative commons
Dimensione
628.91 kB
Formato
Adobe PDF
|
628.91 kB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.


