In this note we show that two nite dimensional algebras have the same representation type if they are stably equivalent of Morita type. Stable equivalences of Morita type were introduced for blocks of group algebras by Brou e 2], see also 7]. The concept is motivated by a result of Rickard. In 9], he proved that any derived equivalence between nite dimensional self-injective algebras and ? indu...

Talk 1: Big Goal of Alg Top, operads and model categories, fix notation for model categories, remarks about how difficult it is to verify model category axioms. Motivation from equivariant spectra, and discussion of Kervaire. Monoidal model categories, define the inherited model structure on the category of algebras over an operad. Basic facts about Bousfield localization. Preservation theorem ...

In our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We study the ‘stable’ properties of the centralizers of S(n − m) in the group algebra C[S(n)] as n → ∞ with m fixed. We construct a limit centralizer algebra A...

We consider the question of ’classificiation’ of finite-dimensional modules over the Jordan algebra R = k〈x, y〉/(xy − yx− y). Complete description of irreducible components of the representation variety mod(R, n) of Jordan algebra is given for any dimension n. It is obtained on the basis of the stratification of this variety related to the Jordan normal form of Y . Any irreducible component of ...

Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...