Modules over a Polynomial Ring Obtained from Representations of a Finite-dimensional Associative Algebra

2005/11/26 by O. N. Popov, Popov, O. N.
Mathematics · #13C14 (Primary) #16E30 (Secondary) #16P10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:13C14 #msc:16E30 #msc:16P10

paper · pdf · doi:10.48550/arxiv.math/0511642

37 pages, AmS-LaTeX, uses Xy-pic

arxiv created 2005/11/26 · arxiv updated 2009/12/01

Abstract

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.

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