@article{Marchuk_2012, title={Generalized Exterior Algebras}, volume={57}, url={https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2021279}, DOI={10.15407/ujpe57.4.422}, abstractNote={<p>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 <em>N</em>-metric exterior algebra, which depends on <em>N</em> 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. <em>N</em>-metric exterior algebras for <em>N </em>≥ 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,<br>especially, in the description of fermions in the presence of a gravity field.</p>}, number={4}, journal={Ukrainian Journal of Physics}, author={Marchuk, N.}, year={2012}, month={Apr.}, pages={422} }