Abstract Building on work of Gerstenhaber, we show that the space integrable derivations an Artin algebra forms a Lie algebra, and restricted if contains field characteristic . We deduce classes in (restricted) is invariant under derived equivalences, stable equivalences Morita type between self‐injective algebras. also provide negative answers to questions about posed by Linckelmann Farkas, Ge...

We study the divergent-sensitive spectrum of weak bisimulation equivalences in the setting of process algebra. To represent the infinite behavior, we consider the prefix iteration extension of a fragment of Milner’s CCS. The prefix iteration operator is a variant on the binary version of the Kleene star operator obtained by restricting the first argument to be an atomic action and allows us to ...

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...

1. Preliminaries about topological model categories 5 2. Preliminaries about equivalences of model categories 9 3. The level model structure on D-spaces 10 4. Preliminaries about π∗-isomorphisms of prespectra 14 5. Stable weak equivalences of D-spectra 18 6. The stable model structure on D-spectra 23 7. Comparisons among P , ΣS , IS , and W T 27 8. Model categories of ring and module spectra 30...

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...

We present a closed model structure for the category of pro-spectra in which the weak equivalences are detected by stable homotopy pro-groups. With some bounded-below assumptions, weak equivalences are also detected by cohomology as in the classical Whitehead theorem for spectra. We establish an Atiyah-Hirzebruch spectral sequence in this context, which makes possible the computation of topolog...