Lie polynomials in an algebra defined by a linearly twisted commutation relation
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We present an elementary approach to characterizing Lie polynomials on the generators [Formula: see text] of an algebra with a defining relation in the form of a twisted commutation relation [Formula: see text]. Here, the twisting map [Formula: see text] is a linear polynomial with a slope parameter, which is not a root of unity. The class of algebras defined as such encompasses [Formula: see text]-deformed Heisenberg algebras, rotation algebras, and some types of [Formula: see text]-oscillator algebras, the deformation parameters of which, are not roots of unity. Thus, we have a general solution for the Lie polynomial characterization problem for these algebras.
1994 ◽
Vol 46
(5)
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pp. 920-929
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1997 ◽
Vol 49
(5)
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pp. 887-915
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2009 ◽
Vol 18
(12)
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pp. 1623-1636
2006 ◽
Vol 15
(10)
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pp. 1245-1277
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1992 ◽
Vol 07
(23)
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pp. 2129-2141
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1998 ◽
Vol 1998
(505)
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pp. 209-235
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1992 ◽
Vol 07
(supp01b)
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pp. 985-1006
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2013 ◽
Vol 55
(A)
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pp. 169-194
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2010 ◽
Vol 19
(06)
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pp. 727-737
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