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The Ext-algebra of standard modules of rhombal algebras.
In his thesis, Michael Peach introduced the infinite dimensional algebra, the rhombal algebra, which is simulatenously quasi-hereditary AND symmetric. Joe Chuang and Will Turner have further generalised his construction to the so called cubist algebras. Moreover, they invented the cubist algebras as families of Koszul pair algebras (instead of the single family introduced by Peach).In this talk, we will mainly concentrate on the rhombal algebras, but will give some reference to the factual or conjectural properties of Ext(\Delta, \Delta) for the cubist algebras. The quiver of the algebra Ext(\Delta,\Delta) for rhombal algebra (and its Koszul dual) will be presented. We in particular calculated a the relations of Ext(\Delta,\Delta) for some subfamilies of rhombal algebras which are closely related to the weight 1 and weight 2 blocks of the symmetric group algebras.
- Speaker
- Aaron Chan (University of Aberdeen)