Modules over a Polynomial Ring Obtained from Representations of a Finite-dimensional Associative Algebra
| dc.creator | Popov, O. N. | |
| dc.date | 2005-11-26 | |
| dc.date.accessioned | 2026-07-07T06:51:45Z | |
| dc.date.available | 2026-07-07T06:51:45Z | |
| dc.description | This is an English translation of the author's Ph.D. thesis, accumulating his results on a construction of Cohen-Macaulay modules over a polynomial ring that appeared in the study of Cauchy-Fueter equations. This construction is generalized from quaternions to arbitrary finite-dimensional associative algebras. We show that for maximally central algebras (as introduced by Azumaya) this construction produces Cohen-Macaulay modules and is an exact functor (tensoring with a bimodule, actually) and this class of algebras cannot be enlarged. For this class several invariants of the resulting modules are calculated via a fairly explicit description of their graded minimal free resolution, that is constructed from the Eagon-Northcott complex. These results have been published in Russ. Math. Surveys and Sbornik: Mathematics but for some proofs, a concise and complete exposition is presented here. | |
| dc.description | 37 pages, AmS-LaTeX, uses Xy-pic | |
| dc.identifier | https://arxiv.org/abs/math/0511642 | |
| dc.identifier | http://arxiv.org/abs/math/0511642 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105093 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13C14 (Primary), 16P10, 16E30 (Secondary) | |
| dc.title | Modules over a Polynomial Ring Obtained from Representations of a Finite-dimensional Associative Algebra | |
| dc.type | text |