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Residue Complex for Sklyanin Algebras of Dimension Three

✍ Scribed by Kaushal Ajitabh

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
197 KB
Volume
144
Category
Article
ISSN
0001-8708

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✦ Synopsis

We describe the residue complex for three-dimensional Sklyanin algebras, which are the interesting special cases of quantum polynomial rings in three variables. In particular, we show that the multiplicities of the point modules in the residue complex are all one, just as in the classical case of commutative polynomial rings in three variables. We explain why the residue complex in the quantum case has the same multiplicities of point modules as that in the commutative case (even if there are fewer point modules in the quantum case) by pointing out two quantum anomalies. 1999 Academic Press Contents. 0. Introduction. 1. Preliminaries. 2. Injective modules of gk-dimension 2. 3. Purity of residue complex. 4. Residue complex and multiplicities of point modules. 5. Comparison with the classical case.

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