TY - JOUR
AU - Marchuk, N.
PY - 2012/04/30
Y2 - 2024/05/19
TI - Generalized Exterior Algebras
JF - Ukrainian Journal of Physics
JA - Ukr. J. Phys.
VL - 57
IS - 4
SE - General problems of theoretical physics
DO - 10.15407/ujpe57.4.422
UR - https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2021279
SP - 422
AB - <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>
ER -