## Simple rings and degree maps

Published in Journal of Algebra

Published in Journal of Algebra

Assume that $X= {x_1,...,x_g}$ is a finite alphabet and $K$ is a field. We study monomial algebras $A= K

Published in Advances in Mathematics

The Grothendieck construction of a diagram X of categories can be seen as a process to construct a single category Gr(X) by gluing categories in the diagram together. Here we formulate diagrams of categories as colax functors from a small category I to the 2-category k-Cat of small k-categories for a fixed commutative ring k. In our previous paper ...

Published in Advances in Mathematics

Let Q be a finite quiver with vertex set I and arrow set Q1, k a field, and kQ its path algebra with its standard grading. This paper proves some category equivalences involving the quotient category QGr(kQ)≔Gr(kQ)/Fdim(kQ) of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, namely QGr(kQ)≡ModS(Q)≡GrL(Q∘)≡ModL...

A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\cal H}(X)$. This well-known line of study is particularly interesting in case $n\eqbd\rank X \ll N$. We enhance this study to an algebra...

Published in Advances in Mathematics

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting.

- ← Previous
- 1
- 2 (current)
- 3
- 4
- Next →