wiki:QuantumDividedPowerAlgebra

The QuantumDividedPowerAlgebra is a graded algebra over a ring R[q]. The component in degree n is the free R[q]-module with basis xn. The multiplication is defined on basis elements by xr.xs = [r+s,r]_q xr+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 R-module with basis xn. The multiplication is defined on basis elements by xr.xs = [r+s,r]_q xr+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 xk> xk x 1 + xk-1 x x + ... 1 x xk (where I have used x as an indeterminate and as a tensor product symbol).

See ticket #11979

Last modified 6 years ago Last modified on 08/21/13 13:08:11

Attachments (1)

  • dividedpower.py (1.8 KB) - added by bruce 7 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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