Exceptional sequences for canonical algebras
Copyright policy )Exceptional sequences for canonical algebras
Let \(\Lambda\) be a canonical algebra with \(n\) simple modules and \({\mathcal D}^ b(\text{mod}(\Lambda))\) the derived category of right \(\Lambda\)- modules. We show that the semidirect product of \(\mathbb{Z}^ n\) and the braid group on \(n\) strings acts transitively on the set of exceptional sequences in \({\mathcal D}^ b(\text{mod}(\Lambda))\). Similar results are proved for coherent sheaves on weighted projective lines.
Representations of orders, lattices, algebras over commutative rings, derived category of right \(\Lambda\)- modules, exceptional sequences, Sheaves, derived categories of sheaves, etc., semidirect products, simple modules, Module categories in associative algebras, coherent sheaves on weighted projective lines, canonical algebras, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Simple and semisimple modules, primitive rings and ideals in associative algebras, braid groups, Vector bundles on surfaces and higher-dimensional varieties, and their moduli
Representations of orders, lattices, algebras over commutative rings, derived category of right \(\Lambda\)- modules, exceptional sequences, Sheaves, derived categories of sheaves, etc., semidirect products, simple modules, Module categories in associative algebras, coherent sheaves on weighted projective lines, canonical algebras, Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers, Simple and semisimple modules, primitive rings and ideals in associative algebras, braid groups, Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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