Узагальнені зовнішні алгебри

Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this work, we define a notion of N-metric exterior algebra, which depends on N matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered a...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2012
Автор: Marchuk, N.
Формат: Стаття
Мова:English
Опубліковано: Publishing house "Academperiodika" 2012
Теми:
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Онлайн доступ:https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2021279
Теги: Додати тег
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Назва журналу:Ukrainian Journal of Physics

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Ukrainian Journal of Physics
Опис
Резюме:Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this work, we define a notion of N-metric exterior algebra, which depends on N matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as a 0-metric exterior algebra. The Clifford algebra can be considered as a 1-metric exterior algebra. N-metric exterior algebras for N ≥ 2 can be considered as generalizations of the Grassmann and Clifford algebras. Specialists consider models of gravity that are based on a mathematical formalism with two metric tensors. We hope that the 2-metric exterior algebra considered in this work can be useful for the development of this model in gravitation theory and,especially, in the description of fermions in the presence of a gravity field.