Generalized Exterior Algebras
DOI:
https://doi.org/10.15407/ujpe57.4.422Keywords:
-Abstract
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.
References
N.G. Marchuk, Field Theory Equations and Clifford Algebras (R&C Dynamics, Izevsk, 2009) (in Russian).
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https://doi.org/10.1007/BF01444648
C. Doran, D. Hestenes, F. Sommen, and N. Van Acker, J. Math. Phys. 34, 3642 (1993).
https://doi.org/10.1063/1.530050
I.M. Benn and R.W. Tucker, An Introduction to Spinors and Geometry with Applications to Physics (Hilger, Bristol, 1987).
P. Lounesto, Clifford Algebras and Spinors (Cambridge Univ. Press, Cambridge, 2001).
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