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

Hideto Nakashima, Takaaki Nomura

3 引用 (Scopus)

### 抄録

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.

元の言語 英語 163-202 40 Kyushu Journal of Mathematics 67 1 https://doi.org/10.2206/kyushujm.67.163 出版済み - 7 25 2013

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Euclidean Jordan Algebra
Jordan Algebra
Multiplication Operator
Unit
Invariant
Vector space
Minor
Euclidean
Determinant
Computing

### All Science Journal Classification (ASJC) codes

• Mathematics(all)

### これを引用

Clans defined by representations of euclidean Jordan algebras and the associated basic relative invariants. / Nakashima, Hideto; Nomura, Takaaki.

：: Kyushu Journal of Mathematics, 巻 67, 番号 1, 25.07.2013, p. 163-202.

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