Cross products, invariants, and centralizers

Benkart, G. ; Elduque, A. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.jalgebra.2016.11.013

Año: 2018

Publicado en: JOURNAL OF ALGEBRA 500 (2018), 69-102
ISSN: 0021-8693

Factor impacto JCR: 0.666 (2018)

Categ. JCR: MATHEMATICS rank: 189 / 313 = 0.604 (2018) - Q3 - T2

Factor impacto SCIMAGO: 1.137 - Algebra and Number Theory (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/FSE
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2013-45588-C3-2-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Algebra (Dpto. Matemáticas)