Reference : Higher trace and Berezinian of matrices over a Clifford algebra
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/9369
Higher trace and Berezinian of matrices over a Clifford algebra
English
Covolo, Tiffany mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Ovsienko, Valentin mailto [CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1]
Poncin, Norbert mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2012
Journal of Geometry and Physics
Elsevier
62
11
2294–2319
Yes (verified by ORBilu)
International
0393-0440
[en] We define the notions of trace, determinant and, more generally, Berezinian of matrices
over a (Z_2)^n-graded commutative associative algebra A. The applications include a new
approach to the classical theory of matrices with coefficients in a Clifford algebra, in
particular of quaternionic matrices. In a special case, we recover the classical Dieudonné
determinant of quaternionic matrices, but in general our quaternionic determinant is
different. We show that the graded determinant of purely even (Z_2)^n-graded matrices of
degree 0 is polynomial in its entries. In the case of the algebra A = H of quaternions, we
calculate the formula for the Berezinian in terms of a product of quasiminors in the sense
of Gelfand, Retakh, and Wilson. The graded trace is related to the graded Berezinian (and
determinant) by a (Z_2)^n-graded version of Liouville’s formula.
http://hdl.handle.net/10993/9369
10.1016/j.geomphys.2012.07.004
http://www.sciencedirect.com.proxy.bnl.lu/science/article/pii/S0393044012001386
http://arxiv.org/abs/1109.5877

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