Grassmann Algebra
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Grassmann Algebra

Grassmann Algebra

Grassmann Algebra

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ExpTheGeneralizedProduct.nb 31<br />

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We can test these formulae by reducing the expressions on either side to scalar products and<br />

tabulating cases. For Λ > p, the first formula gives<br />

Flatten�Table�A � ToScalarProducts�<br />

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�p, 0, 3�, �Λ, p� 1, Min�m, k����<br />

�0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0�<br />

The case of Λ = p is tabulated in the next section.<br />

The second formula can be derived from the first by using the quasi-commutativity of the<br />

generalized product. To check, we tabulate the first few cases:<br />

10.31<br />

Flatten�Table�<br />

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�0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0�<br />

Finally, we can put Μ = Λ - p, and rearrange the above to give:<br />

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�0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,<br />

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0�<br />

� The special case of Λ = p<br />

By putting Λ = p into the first formula of [10.31] we get:<br />

2001 4 26<br />

10.32

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