This book gives an introduction to the representation theory of finite groups and finite
dimensional algebras via homological algebra. In particular, it emphasises common …

We introduce the notion of categorical absorption of singularities: an operation that removes
from the derived category of a singular variety a small admissible subcategory responsible …

The representations of a quiver Q over a field k (the kQ-modules, where kQ is the path
algebra of Q over k) have been studied for a long time, and one knows quite well the …

By work of a number of authors, beginning with Scott and culminating with Galashin and
Lam, the coordinate rings of positroid varieties in the Grassmannian carry cluster algebra …

Generalizing Tate's results for tori, we give closed formulas for the abelian Galois
cohomology groups H^ 1_ {ab}(F, G) and H^ 2_ {ab}(F, G) of a connected reductive group G …

1 Background In our report on the first “Derived Category Methods in Commutative Algebra”
workshop (2008) we wrote:“Derived category methods have proved to be very successful in …

We show that the dimer algebra of a connected Postnikov diagram in the disc is bimodule
internally-Calabi–Yau in the sense of the author's earlier work [43]. As a consequence, we …

An extension $ B\subset A $ of finite dimensional algebras is bounded if the $ B $-$ B $-
bimodule $ A/B $ is $ B $-tensor nilpotent, its projective dimension is finite and $\mathrm …

It has been conjectured that the hemisphere partition function arXiv: 1308.2217, arXiv:
1308.2438 in a gauged linear sigma model (GLSM) computes the central charge arXiv …

We investigate the (separated) monomorphism category mono (Q, Λ) $\operatorname
{mono}(Q,\Lambda) $ of a quiver over an Artin algebra Λ $\Lambda $. We show that there …