… By a k-representation of G we mean a finite dimensional … a complete local ring with residue
field k, then a deformation of V in … We denote by Def(V, A) the set of such deformations. Let V …

… deformations and (uni)versal deformation rings of complexes over finite dimensional algebras
… As a consequence, we obtain that universal deformation rings of complexes whose terms …

… , and if n ≥ m, then n = m, and R is a complete intersection and finite flat over W(F). If the
ring R in the lemma was a universal deformation ring for certain deformation types of a given …

… In §2, we review some preliminary definitions and properties concerning deformations and
(uni)versal deformation rings of modules over finite dimensional algebras as discussed in [8], …

… R ( Λ , V • ) which is a complete local commutative Noetherian k-algebra with residue field
k. … Λ and another finite dimensional k-algebra Γ preserve these versal deformation rings. …

… Hence this enables us to use methods from the representation theory of finite dimensional
algebras to study deformation rings of group representations. This approach has recently led …

… In Section 2, we give an introduction to versal and universal deformation rings and
deformations of finitely generated modules V for a finite dimensional k-algebra Λ. In particular, we …

… Although the present book centers on the finite dimensional algebra approach to quantum
groups, it also takes up two other, important, related topics. First, following [59], we use …

… Universal localisations for finite dimensional algebras … properties of universal localisations
for finite dimensional K -algebras. It turns out that we can define universal localisations with …

… Two very important properties of Λ are the following: Firstly, in general, if Λ is a periodic finite
dimensional algebra, then every nonprojective module is periodic with period dividing the …