Simple Algebras of Invariant Operators

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: comtrans algebras Jordan algebras Lie algebras invariant operators
• 年，卷（期）: 2001,（3）
• 页码范围: 285-292
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Comtrans algebras were introduced in as algebras with two trilinear operators, a commutator [x, y, z] and a translator <x, y, z>, which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of hermitian operators over a field with a minimum polynomial x2+1. This paper is about generalizing the hermitian case to the so-called invariant case. The main result of this paper shows that the vector space of n-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.