Geodesic
Two-step tilting for standardly stratified algebras
Algebra and discrete mathematics, no. 3 (2004), pp. 38-59

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We study the class of standardly stratified algebras introduced by Cline, Parshall and Scott, and its subclass of the so-called weakly properly stratified algebras, which generalizes the class of properly stratified algebras introduced by Dlab. We characterize when the Ringel dual of a standardly stratified algebra is weakly properly stratified and show the existence of a two-step tilting module. This allows us to calculate the finitistic dimension of such algebras. Finally, we also give a construction showing that each finite partially pre-ordered set gives rise to a weakly properly stratified algebras with a simple preserving duality.
Keywords: stratified algebra, two-step tilting, finitistic dimension. 
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     author = {Anders Frisk},
     title = {Two-step tilting for standardly stratified algebras},
     journal = {Algebra and discrete mathematics},
     pages = {38--59},
     publisher = {mathdoc},
     number = {3},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2004_3_a3/}
}
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Anders Frisk. Two-step tilting for standardly stratified algebras. Algebra and discrete mathematics, no. 3 (2004), pp. 38-59. http://geodesic.mathdoc.fr/item/ADM_2004_3_a3/