Clans defined by representations of euclidean Jordan algebras and the associated basic relative invariants

Hideto Nakashima, Takaaki Nomura

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Starting with a representation φ{symbol} of a Euclidean Jordan algebra V by selfadjoint operators on a real Euclidean vector space E, we introduce a clan structure in VE: = E ⊕ V. By the adjunction of a unit element to VE, we obtain a clan V 0E with unit element. By computing the determinant of the right multiplication operators of V 0 E, we get an explicit expression of the basic relative invariants of V 0E in terms of the Jordan algebra principal minors of V and the quadratic map associated with φ{symbol}. For the dual clan of V 0 E, we also obtain an explicit expression of the basic relative invariants in a parallel way.

Original languageEnglish
Pages (from-to)163-202
Number of pages40
JournalKyushu Journal of Mathematics
Volume67
Issue number1
DOIs
Publication statusPublished - Jul 25 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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