Abstract
Until now we only considered the algebra of Grassmann-valued expressions and differentiation and integration with respect to Grassmann variables. We kept away from transformations between even and odd variables. This will now be done. In fact, symmetries will be observed, which include both types of variables. To begin with we use the differential, which immediately leads to matrices with elements of both even and odd elements. We generalize the transposition, the determinant, and the trace to its superforms.
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References
F.A. Berezin, Introduction to Superanalysis (Springer, Reidel, Dordrecht, 1987)
B. DeWitt, Supermanifolds (Cambridge University Press, Cambridge,1984)
V. Rittenberg, M. Scheunert, Elementary construction of graded Lie groups. J. Math. Phys. 19, 709 (1978)
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Wegner, F. (2016). Supermatrices. In: Supermathematics and its Applications in Statistical Physics. Lecture Notes in Physics, vol 920. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49170-6_10
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DOI: https://doi.org/10.1007/978-3-662-49170-6_10
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-662-49170-6
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