The QuantumDividedPowerAlgebra is a graded algebra over a ring R[q]. The component in degree n is the free R[q]module with basis x^{n}. The multiplication is defined on basis elements by x^{r}.x^{s} = [r+s,r]_q x^{r+s} where [r+s,r]_q is the quantum binomial coefficient.
The DividedPowerAlgebra is a graded algebra over a ring R. The component in degree n is the free Rmodule with basis x^{n}. The multiplication is defined on basis elements by x^{r}.x^{s} = [r+s,r]_q x^{r+s} where [r+s,r] is the binomial coefficient.
The divided power algebra is a Hopf algebra and is the dual Hopf algebra to R[x]. The coproduct on the divided power Hopf algebra is x^{k}> x^{k} x 1 + x^{k1} x x + ... 1 x x^{k} (where I have used x as an indeterminate and as a tensor product symbol).See ticket #11979
Last modified 8 years ago
Last modified on 08/21/13 13:08:11
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dividedpower.py (1.8 KB)  added by 10 years ago.
This file is my attempt at a minimal implementation of the divided power algebra. This does not work. It appears to confuse integers (the basis) with using integers as coefficients.
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