## Galois groups and connection matrices for $$q$$-difference equations.(English)Zbl 0844.12004

Summary: We study the Galois group of a matrix $$q$$-difference equation with rational coefficients which is regular at $$0$$ and $$\infty$$, in the sense of (difference) Picard-Vessiot theory, and show that it coincides with the algebraic group generated by matrices $$C(z) C(w)^{-1}$$, $$z, w \in C^*$$, where $$C(z)$$ is the Birkhoff connection matrix of the equation.

### MSC:

 12H10 Difference algebra 39A10 Additive difference equations
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### References:

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