TY - JOUR

T1 - Clans defined by representations of euclidean Jordan algebras and the associated basic relative invariants

AU - Nakashima, Hideto

AU - Nomura, Takaaki

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/7/25

Y1 - 2013/7/25

N2 - 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.

AB - 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.

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U2 - 10.2206/kyushujm.67.163

DO - 10.2206/kyushujm.67.163

M3 - Article

AN - SCOPUS:84880812420

SN - 1340-6116

VL - 67

SP - 163

EP - 202

JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

IS - 1

ER -