Abstract
We construct the quantum supergroupGL q(1/1) in its matrix representation. We investigate properties of powers of 2×2 quantum super-matrices and we show that any element ofGL q(1/1) can be written as the exponential of a matrix with non-commuting entries. An explicit construction of this exponential form is presented. Finally, we prove a relation between the quantum superdeterminant of a quantum matrix and the supertrace of the logarithm of the quantum matrix.
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