A construction of dual box

Serge Ovsienko

Algebra and discrete mathematics, no. 2 (2006), pp. 77-86.

Résumé

Let $\mathtt{R}$ be a quasi-hereditary algebra, $\mathcal{F}(\mathrm{\Delta })$ and $\mathcal{F}(\mathrm{\nabla })$ its categories of good and cogood modules correspondingly. In [6] these categories were characterized as the categories of representations of some boxes $\mathcal{A}={\mathcal{A}}_{\mathrm{\Delta }}$ and ${\mathcal{A}}_{\mathrm{\nabla }}$. These last are the box theory counterparts of Ringel duality [8]. We present an implicit construction of the box $\mathcal{B}$ such that $\mathcal{B}-\mathrm{mo}$ is equivalent to $\mathcal{F}(\mathrm{\nabla })$.

Détail

Mots-clés : box, derived category, differential graded category.