{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T04:53:12Z","timestamp":1648615992789},"reference-count":26,"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":[[2021,2]]},"abstract":"<jats:p> We consider the algebra of invariants of [Formula: see text]-tuples of [Formula: see text] matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic [Formula: see text] different from two. It is well known that this algebra is generated by the coefficients of the characteristic polynomial of all products of generic and transpose generic [Formula: see text] matrices. We establish that in case [Formula: see text] the maximal degree of indecomposable invariants tends to infinity as [Formula: see text] tends to infinity. In other words, there does not exist a constant [Formula: see text] such that it only depends on [Formula: see text] and the considered algebra of invariants is generated by elements of degree less than [Formula: see text] for any [Formula: see text]. This result is well-known in case of the action of the general linear group. On the other hand, for the rest of [Formula: see text] the given phenomenon does not hold. We investigate the same problem for the cases of symmetric and skew-symmetric matrices. <\/jats:p>","DOI":"10.1142\/s0218196721500089","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T07:57:50Z","timestamp":1602748670000},"page":"161-171","source":"Crossref","is-referenced-by-count":0,"title":["Indecomposable orthogonal invariants of several matrices over a field of positive characteristic"],"prefix":"10.1142","volume":"31","author":[{"given":"Artem","family":"Lopatin","sequence":"first","affiliation":[{"name":"State University of Campinas, 651 Sergio Buarque de Holanda, 13083-859 Campinas, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,11,24]]},"reference":[{"key":"S0218196721500089BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2005.02.011"},{"key":"S0218196721500089BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.09.018"},{"key":"S0218196721500089BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/03081080701669333"},{"issue":"1","key":"S0218196721500089BIB004","first-page":"37","volume":"7","author":"\u0110okovi\u0107 D. \u017d.","year":"2012","journal-title":"Int. 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