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Isomorphisms between quantum generalized Weyl algebras. (English) Zbl 1102.16025

Generalized Weyl algebras \(A\) were introduced by V. V. Bavula [St. Petersbg. Math. J. 4, No. 1, 71-92 (1993); translation from Algebra Anal. 4, No. 1, 75-97 (1992; Zbl 0807.16027)] in the following way. Let \(R\) be an associative algebra with a non-central element \(a\) and with an automorphism \(\sigma\). Then \(A\) is an iterated skew polynomial extension \(R[x,y;\sigma]\) where \(xr=\sigma(r)x\), \(yr=\sigma^{-1}(r)y\), \(xy=\sigma(a)\), \(yx=a\). The authors consider the quantum case when \(R=k[h]\), \(k\) is a field and \(\sigma(h)=qh\), where \(q\in k^*\) is not a root of 1. In this case there is found a criterion under which two quantum generalized Weyl algebras are isomorphic.

MSC:

16W35 Ring-theoretic aspects of quantum groups (MSC2000)
16S36 Ordinary and skew polynomial rings and semigroup rings
16S32 Rings of differential operators (associative algebraic aspects)

Citations:

Zbl 0807.16027
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References:

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