Timeline for How to recognize a finite dimensional algebra is Koszul or quadratic?
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Jul 21, 2011 at 2:56 | comment | added | Benjamin Steinberg | I looked at the paper of Dlab et al, where standard Koszul is introduced. They say you need a linear resolution of both left and right standard modules. For directed quasihereditary algebras the standard modules on one side are projective and on the other side simple. So if I understood rightly, the standard Koszul is equivalent to Koszul in the directed case. They also point out in the paper it suffices to show the Ext algebra is generated in degrees zero and one. I might be able to determine this. I know how to explicitly construct all extensions of one simple by another. | |
Jul 21, 2011 at 1:38 | comment | added | Benjamin Steinberg | Thanks. In my case the quasihereditary structure is directed, so the standard modules are projective indecomposables. I am not a specialist in finite dimensional algebras, but it would seem to me that in this case standard Koszul and Koszul should be the same. Is that correct? | |
Jul 20, 2011 at 18:40 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |