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Quasi-deformations of \(\mathfrak{sl}_2(\mathbb F)\) using twisted derivations. (English) Zbl 1131.17010

In their previous paper in [J. Fuchs (ed.) et al., Noncommutative geometry and representation theory in mathematical physics. Contemp. Math. 391, 241–248 (2005; Zbl 1105.17005)] the authors introduced the notion of a quasi-deformation of an algebra using \(\sigma\)-derivations where \(\sigma\) is an endomorphism of the algebra. In the present paper the method of quasi-deformation being applied to the Lie algebras \(sl_2\) shows that one can obtain the Heisenberg Lie algebra as its quasi-deformation. Another example is a quasi-deformation of a polynomial algebra in \(t\) factorized by the ideal generated by \(t^3\). It is shown that in comparison with classical deformations by quasi-deformations one can obtain a larger class of algebras.

MSC:

17B66 Lie algebras of vector fields and related (super) algebras

Citations:

Zbl 1105.17005
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