Йорданова алгебра

Йорданова алгебра — (неассоциативная) алгебра над кольцом, в которой справедливы тождества

  1. (коммутативность)
  2. (йорданово тождество)

Йордановы алгебры были Паскуалем Йорданом в 1933 году для аксиоматизации основ квантовой механики, точнее, для формализации понятия алгебры квантовых наблюдаемых. Они были изначально названы «r-системы счисления». Термин йордановы алгебры ввёл Абрахам Альберт в 1946 при систематическом их изучении.

Примеры

Пусть  — ассоциативная алгебра над полем характеристики . Множество с операциями сложения и йорданова умножения

образует алгебру , которая является йордановой. Такие алгебры называются специальными йордановыми алгебрами.

Ссылки

Литература

  • Кон П. Глава VII, §7. // Универсальная алгебра. — М.: Мир, 1969. — С. 316—328. — 351 с.
  • Мельников О. В.; Ремесленников В. Н.; Романьков В. А.; Скорняков Л. А.; Шестаков И. П. Глава 3, §7. Кольца и модули с дополнительной структурой // Общая алгебра / Скорняков Л. А.. — М.: Наука, 1990. — Т. 1. — С. 404—419. — 592 с. — (Справочная математическая библиотека). — 30 000 экз. — ISBN 5-02-014426-6.

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