Poincare series of some pure and mixed trace algebras of two generic matrices

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dc.creatorDjokovic, Dragomir Z.
dc.date2006-09-09
dc.date.accessioned2026-07-07T12:53:16Z
dc.date.available2026-07-07T12:53:16Z
dc.descriptionWe work over a field K of characteristic zero. The Poincare series for the algebra C_{n,2} of GL_n-invariants and the algebra T_{n,2} of GL_n-concomitants of two generic n x n matrices x and y are presented for n less than or equal 6. Both simply graded and bigraded cases are included. The cases for n at most 4 were known previously. If n=5 or 6, we show that C_{n,2} has no bigraded system of parameters. For the algebra C_{4,2} and C_{5,2} we construct a minimal set of generators and give an application to Specht's theorem on unitary similarity of two complex matrices. Five conjectures are proposed concerning the numerators and denominators of various Poincare series mentioned above. Some heuristic formulas and open problems are stated.
dc.description28 pages, 12 tables
dc.identifierhttps://arxiv.org/abs/math/0609262
dc.identifierhttp://arxiv.org/abs/math/0609262
dc.identifierJournal of Algebra 309 (2007), 654-671
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223566
dc.subjectCommutative Algebra
dc.subject13A50; 14L35; 20G20
dc.titlePoincare series of some pure and mixed trace algebras of two generic matrices
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