Group gradings on the Jordan algebra of upper triangular matrices

Let G be an arbitrary group and let K be a field of characteristic different from 2. We classify the G-gradings on the Jordan algebra UJn of upper triangular matrices of order n over K. It turns out that there are, up to a graded isomorphism, two families of gradings: the elementary gradings (analog...

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Bibliographic Details
Published in:Linear algebra and its applications 2017-12, Vol.534, p.1-12
Main Authors: Koshlukov, Plamen, Yasumura, Felipe Yukihide
Format: Article
Language:English
Subjects:
Academic grading
Group gradings
Group theory
Isomorphism
Jordan algebras
Linear algebra
Matrix
Polynomials
Upper triangular matrices
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Summary:Let G be an arbitrary group and let K be a field of characteristic different from 2. We classify the G-gradings on the Jordan algebra UJn of upper triangular matrices of order n over K. It turns out that there are, up to a graded isomorphism, two families of gradings: the elementary gradings (analogous to the ones in the associative case), and the so called mirror type (MT) gradings. Moreover we prove that the G-gradings on UJn are uniquely determined, up to a graded isomorphism, by the graded identities they satisfy.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.08.004