Torsion-type q-deformed Heisenberg algebra and its Lie polynomials
Abstract
Given a scalar parameter q, the q-deformed Heisenberg algebra H(q) is the unital associative algebra with two generators A,B that satisfy the q-deformed commutation relation AB-qBA= I, where I is the multiplicative identity. For H(q) of torsion-type, that is if q is a root of unity, characterization is obtained for all the Lie polynomials in A,B and basis and graded structure and commutation relations for associated Lie algebras are studied.
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