**Integration On An Exterior Algebra**

Let be the exterior algebra of polynomials in anticommuting elements over the field of complex numbers. (The ordering of the generators is fixed and defines the orientation of the exterior algebra.) The **Berezin integral** on is the linear functional with the following properties:

for any where means the left or the right partial derivative. These properties define the integral uniquely. The formula

expresses the Fubini law. On the right-hand side, the interior integral of a monomial is set to be where ; the integral of vanishes. The integral with respect to is calculated in the similar way and so on.

Read more about this topic: Berezin Integral

### Famous quotes containing the words algebra, integration and/or exterior:

“Poetry has become the higher *algebra* of metaphors.”

—José Ortega Y Gasset (1883–1955)

“Look back, to slavery, to suffrage, to *integration* and one thing is clear. Fashions in bigotry come and go. The right thing lasts.”

—Anna Quindlen (b. 1952)

“This idoll which you terme Virginitie,

Is neither essence subject to the eie,

No, nor to any one *exterior* sence,

Nor hath it any place of residence,

Nor is’t of earth or mold celestiall,

Or capable of any forme at all.”

—Christopher Marlowe (1564–1593)