Abstract
We consider the algebras, with two generators a and b, generated by the quadratic relations ba = α2 + βab + γb2, where the coefficients α, β, and γ belong to an arbitrary field F of characteristic 0. We find conditions for such an algebra to be expressed as a skew polynomial algebra with generator b over the polynomial ring F [a]. These conditions are equivalent to the existence of the Poincaree-Birkhoff-Witt basis, i. e., basis of the form {am, bn}. Bibliography: 16 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 144–171.
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Golovashkin, A.V., Maximov, V.M. On Algebras of Skew Polynomials Generated by Quadratic Homogeneous Relations. J Math Sci 129, 3757–3771 (2005). https://doi.org/10.1007/s10958-005-0311-z
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DOI: https://doi.org/10.1007/s10958-005-0311-z