## 11 Citations

### Extension Algebras of Standard Modules

- Mathematics
- 2013

Let A be a basic finite-dimensional k-algebra standardly stratified for a partial order ≤and Δ be the direct sum of all standard modules. In this article, we study the extension algebra of standard…

### Quasi-hereditary covers of higher zigzag-algebras

- Mathematics
- 2018

The aim of this paper is to define and study some quasi-hereditary covers for higher zigzag algebras. We will show how these algebras satisfy three different Koszul properties: they are Koszul in the…

### Quasi-hereditary covers and derived equivalences of higher zigzag algebras

- Mathematics
- 2018

In this thesis we look at higher zigzag algebras Zds of type A as a generalization of Brauer tree algebras whose tree is a line. We recall the presentation of these algebras as path algebras with…

### Q-Koszul Algebras and Three Conjectures

- Mathematics
- 2014

In previous work, the authors introduced the notion of Q-Koszul algebras, as a tool to "model" module categories for semisimple algebraic groups over fields of large characteristics. Here we suggest…

### Some Homological Properties of Tensor and Wreath Products of Quasi-Hereditary Algebras

- Mathematics
- 2012

We show that taking the wreath product of a quasi-hereditary algebra with the symmetric group inherits several homological properties of the original algebra, namely BGG duality, standard Koszulity,…

### Further Properties of Koszul Pairs and Applications

- Mathematics
- 2015

In this paper we continue the study of Koszul pairs, focusing on new applications. First, we prove in a unifying way several equivalent descriptions of Koszul rings, some of them being well known in…

### Further Properties and Applications of Koszul Pairs

- Mathematics
- 2016

Koszul pairs were introduced in (arXiv:1011.4243) as an instrument for the study of Koszul rings. In this paper, we continue the enquiry of such pairs, focusing on the description of the second…

### A generalized Koszul theory and its applications in representation theory.

- Mathematics
- 2012

University of Minnesota Ph.D. dissertation. August 2012. Major: Mathematics. Advisor: Liping Li. 1 computer file (PDF); iii, 128 pages.

## References

SHOWING 1-10 OF 23 REFERENCES

### The Weyl extension algebra of $GL_2(\bar{\mathbb{F}}_p)$.

- Mathematics
- 2011

We compute the Yoneda extension algebra of the collection of Weyl modules for $GL_2$ over an algebraically closed field of positive characteristic p by developing a theory of generalised Koszul…

### The Coinvariant Algebra and Representation Types of Blocks of Category O

- Mathematics
- 2001

Let G be a finite‐dimensional semisimple Lie algebra over the complex numbers. Let A be the finite‐dimensional algebra of a (regular or singular) block of the BGG‐category O. By results of Soergel, A…

### Some homological properties of the category O

- Mathematics
- 2007

In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For…

### Category : Quivers and endomorphism rings of projectives

- Mathematics
- 2003

We describe an algorithm for computing quivers of category O of a finite dimensional semisimple Lie algebra. The main tool for this is Soergel’s description of the endomorphism ring of the…

### Representations of Semisimple Lie Algebras in the BGG Category O

- Mathematics
- 2008

Review of semisimple Lie algebras Highest weight modules: Category $\mathcal{O}$: Basics Characters of finite dimensional modules Category $\mathcal{O}$: Methods Highest weight modules I Highest…

### On Auslander-Reiten translates in functorially finite subcategories and applications

- Mathematics
- 2010

Functorially finite subcategories in module categories over Artin algebras have been introduced by Auslander and Smalø [2] to provide a convenient setting for existence of relative Auslander-Reiten…