Generalized Exterior Algebras


  • N. Marchuk Steklov Mathematical Institute of Russian Academy of Sciences





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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How to Cite

Marchuk, N. (2012). Generalized Exterior Algebras. Ukrainian Journal of Physics, 57(4), 422.



General problems of theoretical physics