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Group gradings on the Jordan algebra of upper triangular matrices

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Abstract 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 UJ n of upper… Click to show full abstract

Abstract 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 UJ n 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 UJ n are uniquely determined, up to a graded isomorphism, by the graded identities they satisfy.

Keywords: triangular matrices; jordan algebra; algebra upper; group; gradings jordan; upper triangular

Journal Title: Linear Algebra and its Applications
Year Published: 2017

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