| Shrnutí: | <p>We prove an analogue of a theorem of Avrunin and Scott for truncated polynomial algebras <em>Λ<sub>m</sub></em>:=<em>k</em>[<em>X</em><sub>1</sub>,...,<em>X<sub>m</sub></em>]/(<em>X<sup>2</sup><sub style="position: relative; left: -.5em;">i</sub></em>) over an algebraically closed field of arbitrary characteristic. The Avrunin and Scott theorem relates the support variety for a finite-dimensional <em>kE</em>-module to its rank variety (where char(<em>k</em>)=<em>p</em> and <em>E</em> is an elementary abelian <em>p</em>-group). The analogue of the Avrunin and Scott theorem relates the support variety for a finite-dimensional <em>Λ<sub>m</sub></em>-module (using Hochschild cohomology) to its rank variety (developed in [K. Erdmann, M. Holloway, Rank varieties and projectivity for a class of local algebras, Math. Z. 247 (2004) 441–460] using Clifford algebras). Along the way to proving our main result we provide a new proof of the Avrunin and Scott theorem for elementary abelian <em>p</em>-group algebras which we are then able to generalise to the setting of <em>Λ<sub>m</sub></em>-algebras.</p>
|
|---|