Deformed preprojective algebras of type L: Külshammer spaces and derived equivalences
نویسندگان
چکیده
منابع مشابه
Lecture 17: Deformed Preprojective Algebras
(1) If there is an indecomposable representation of dimension v, then v is a root. (2) If v is a real root, then there is a unique (up to an isomorphism) indecomposable representation of dimension v. (3) If v is primitive (meaning that GCD(vi) = 1) and there is an indecomposable representation of dimension v, then pv, the number of parameters for the isomorphism classes of indecomposable repres...
متن کاملDerived equivalences and Gorenstein algebras
In this note, we introduce the notion of Gorenstein algebras. Let R be a commutative Gorenstein ring and A a noetherian R-algebra. We call A a Gorenstein R-algebra if A has Gorenstein dimension zero as an R-module (see [2]), add(D(AA)) = PA, where D = HomR(−, R), and Ap is projective as an Rpmodule for all p ∈ Spec R with dim Rp < dim R. Note that if dim R = ∞ then a Gorenstein R-algebra A is p...
متن کاملDouble Hall Algebras and Derived Equivalences
The resulting algebra is known as the Hall algebra HA of A. Hall algebras first appeared in the work of Steinitz [S] and Hall [H] in the case where A is the category of Abelian p-groups. They reemerged in the work of Ringel [R1]-[R3], who showed in [R1] that when A is the category of quiver representations of an A-D-E quiver ~ Q over a finite field Fq, the Hall algebra of A provides a realizati...
متن کاملEquivalences of Derived Categories for Symmetric Algebras
It is about a decade since Broué made his celebrated conjecture [2] on equivalences of derived categories in block theory: that the module categories of a block algebra A of a finite group algebra and its Brauer correspondent B should have equivalent derived categories if their defect group is abelian. Since then, character-theoretic evidence for the conjecture has accumulated rapidly, but unti...
متن کاملGeneralisations of Preprojective algebras
In this thesis, we investigate two ways of generalising the preprojective algebra. First, we introduce the multiplicative preprojective algebra, Λ(Q), which is a multiplicative analogue of the deformed preprojective algebra, introduced by Crawley-Boevey and Holland. The special case q = 1 is the undeformed multiplicative preprojective algebra, which is an analogue of the ordinary (undeformed) p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.08.024