Generalized Exterior Algebras

Authors

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

DOI:

https://doi.org/10.15407/ujpe57.4.422

Keywords:

-

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).

H. Grassmann, Math. Commun. 12, 375 (1877).

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).

https://doi.org/10.1017/CBO9780511526022

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Published

2012-04-30

How to Cite

Marchuk, N. (2012). Generalized Exterior Algebras. Ukrainian Journal of Physics, 57(4), 422. https://doi.org/10.15407/ujpe57.4.422

Issue

Section

General problems of theoretical physics