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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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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Publishing house "Academperiodika"
2012
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| Subjects: | |
| Online Access: | https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2021279 |
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| Summary: | 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. |
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