Quasi-hereditary algebras and generalized Koszul duality

@article{Madsen2012QuasihereditaryAA,
  title={Quasi-hereditary algebras and generalized Koszul duality},
  author={Dag Oskar Madsen},
  journal={Journal of Algebra},
  year={2012},
  volume={395},
  pages={96-110}
}
  • D. Madsen
  • Published 2 January 2012
  • Mathematics
  • Journal of Algebra

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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

Koszul duality for extension algebras of standard modules

On a common generalization of Koszul duality and tilting equivalence

The Weyl extension algebra of GL2(F¯p)

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

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

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

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

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

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

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