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### Skew commuting variables

I want to work in the ring QQ<x0, x1, x2> / (xi*xj = -xj*xi for i \neq j). (In particular, xi^2 \neq 0; this is not the exterior algebra.)

I seems like FreeAlgebraQuotient is the thing to use, but I am not sure how. In the documentation for FreeAlgebraQuotient, the algebras are 4-dimensional as modules over QQ. However in my application, the algebra is infinite-dimensional as a module, so I can't write down the matrices for the action of the generators.

Is there another way to obtain this ring? Thanks.

 2 retagged FrédéricC 2539 ●3 ●28 ●53

### Skew commuting variables

I want to work in the ring QQ<x0, x1, x2> / (xi*xj = -xj*xi for i \neq j). (In particular, xi^2 \neq 0; this is not the exterior algebra.)

I seems like FreeAlgebraQuotient is the thing to use, but I am not sure how. In the documentation for FreeAlgebraQuotient, the algebras are 4-dimensional as modules over QQ. However in my application, the algebra is infinite-dimensional as a module, so I can't write down the matrices for the action of the generators.

Is there another way to obtain this ring? Thanks.