Abstract
In my note I will present some results in joint work [IW] with Michael Wemyss on special Cohen-Macaulay modules. We start with explaining briefly the background in noncommutative algebra. After Auslander [A], algebras of finite global dimension are one of the most important subjects in representation theory. For example, famous Auslander-Reiten theory [Y] is based on certain algebras of global dimension two, called Auslander algebras (e.g. see [I]). We will explain the connection to special Cohen-Macaulay modules. I recommend anyone who is interested in non-commutative algebra to learn the work of Auslander (especially [A], which is available in [A2]). Additionally, my recent trial [I] to extend this a little bit.
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