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Twisted Traces and Positive Forms on Generalized $q$-Weyl Algebras
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $\mathcal{A}$ be a generalized $q$-Weyl algebra, it is generated by $u$, $v$, $Z$, $Z^{-1}$ with relations $ZuZ^{-1}=q^2u$, $ZvZ^{-1}=q^{-2}v$, $uv=P\big(q^{-1}Z\big)$, $vu=P(qZ)$, where $P$ is a Laurent polynomial. A Hermitian form $(\cdot,\cdot)$ on $\mathcal{A}$ is called invariant if $(Za,b)=\big(a,bZ^{-1}\big)$, $(ua,b)=(a,sbv)$, $(va,b)=\big(a,s^{-1}bu\big)$ for some $s\in \mathbb{C}$ with $|s|=1$ and all $a,b\in \mathcal{A}$. In this paper we classify positive definite invariant Hermitian forms on generalized $q$-Weyl algebras.
Keywords: trace, inner product, star-product.
Mots-clés : quantization 
@article{SIGMA_2022_18_a8,
     author = {Daniil Klyuev},
     title = {Twisted {Traces} and {Positive} {Forms} on {Generalized} $q${-Weyl} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a8/}
}
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Daniil Klyuev. Twisted Traces and Positive Forms on Generalized $q$-Weyl Algebras. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a8/

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