An extension of a [formula omitted]-deformed Heisenberg algebra and its Lie polynomials

Abstract

Let F be a field, and fix a q∈F. The q-deformed Heisenberg algebra H(q) is the unital associative algebra over F with generators A, B and a relation which asserts that AB−qBA is the multiplicative identity in H(q). We extend H(q) into an algebra R(q) defined by generators A, B and a relation which asserts that AB−qBA is central in R(q). We identify all elements of R(q) that are Lie polynomials in A, B.