Calculus of Finite Differences - eDisk
Calculus of Finite Differences - eDisk
Calculus of Finite Differences - eDisk
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– p. 7/?Definition <strong>of</strong> down-up algebrasUnfortunately these algebras are defined by generatorsand relations. We use C as our ground field. Fix apolynomial f ∈ C[x] and scalars r,s,γ ∈ C. Thedown-up algebra L = L(f,r,s,γ) is generated byelements d, u, and h, subject to the relations:hu − ruh = γudh − rhd = γddu − sud = f(h).Think <strong>of</strong> d as a down operator, u as an up operator,and h as a horizontal or sideways operator.