Open AccessGeneralized Exterior Algebras
Author(s) -
Н. Г. Марчук
Publication year - 2012
Publication title -
ukrainian journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.213
H-Index - 17
eISSN - 2071-0194
pISSN - 2071-0186
DOI - 10.15407/ujpe57.4.422
Subject(s) - clifford algebra , exterior algebra , algebra over a field , mathematics , formalism (music) , metric (unit) , geometric algebra , algebra representation , pure mathematics , differential form , art , musical , operations management , economics , visual arts
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.