{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T18:48:52Z","timestamp":1773254932601,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p> The trace algebra C<jats:sub>nd<\/jats:sub> over a field of characteristic 0 is generated by all traces of products of d generic n \u00d7 n matrices, n, d \u2265 2. Minimal sets of generators of C<jats:sub>nd<\/jats:sub> are known for n = 2 and 3 for any d and for n = 4 and 5 and d = 2. The explicit defining relations between the generators are found for n = 2 and any d and for n = 3, d = 2 only. Defining relations of minimal degree for n = 3 and any d are also known. The minimal degree of the defining relations of any homogeneous minimal generating set of C<jats:sub>42<\/jats:sub> is equal to 12. Starting with the generating set given recently by Drensky and Sadikova, we have determined all relations of degree \u2264 14. For this purpose we have developed further algorithms based on representation theory of the general linear group and easy computer calculations with standard functions of Maple. <\/jats:p>","DOI":"10.1142\/s0218196709004981","type":"journal-article","created":{"date-parts":[[2009,2,25]],"date-time":"2009-02-25T10:55:38Z","timestamp":1235559338000},"page":"107-127","source":"Crossref","is-referenced-by-count":4,"title":["DEFINING RELATIONS OF LOW DEGREE OF INVARIANTS OF TWO 4 \u00d7 4 MATRICES"],"prefix":"10.1142","volume":"19","author":[{"given":"VESSELIN","family":"DRENSKY","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria"}]},{"given":"ROBERTO","family":"LA SCALA","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Bari, Via E. Orabona 4, 70125 Bari, Italia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1080\/00927878908823740"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(85)90183-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.01.042"},{"key":"rf4","first-page":"103","volume":"60","author":"Benanti F.","journal-title":"C. R. Acad. Bulg. 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