70698 20191127155455.0 doi 10.1016/j.jalgebra.2016.11.013 sideral 105220 ART-2018-105220 eng Benkart, G. Cross products, invariants, and centralizers 2018 Access copy available to the general public Unrestricted An algebra V with a cross product x has dimension 3 or 7. In this work, we use 3-tangles to describe, and provide a basis for, the space of homomorphisms from V-circle times n to V-circle times m that are invariant under the action of the automorphism group Aut(V, x) of V, which is a special orthogonal group when dim V = 3, and a simple algebraic group of type G(2) when dim V = 7. When m = n, this gives a graphical description of the centralizer algebra End(Aut(v, x))(V-circle times n), and therefore, also a graphical realization of the Aut(V, x)-invariants in V-circle times 2n equivalent to the First Fundamental Theorem of Invariant Theory. We show how the 3-dimensional simple Kaplansky Jordan superalgebra can be interpreted as a cross product (super)algebra and use 3-tangles to obtain a graphical description of the centralizers and invariants of the Kaplansky superalgebra relative to the action of the special orthosymplectic group. info:eu-repo/grantAgreement/ES/DGA/FSE info:eu-repo/grantAgreement/ES/MINECO/MTM2013-45588-C3-2-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.666 2018 MATHEMATICS 189 / 313 = 0.604 2018 Q3 T2 1.137 2018 Algebra and Number Theory 2018 Q1 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0002-6497-2162 Elduque, A. Universidad de Zaragoza 2006 005 Universidad de Zaragoza Dpto. Matemáticas Área Algebra 500 (2018), 69-102 J. algebra JOURNAL OF ALGEBRA 0021-8693 312286 http://zaguan.unizar.es/record/70698/files/texto_completo.pdf Postprint 69516 http://zaguan.unizar.es/record/70698/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:70698 articulos driver 2019-11-27-15:47:05 ARTICLE