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 ![]() | |
Ovsienko, Valentin ![]() | |
Poncin, Norbert ![]() | |
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 |
File(s) associated to this reference | ||||||||||||||
Fulltext file(s):
| ||||||||||||||
All documents in ORBilu are protected by a user license.