Get an algebra that allows generators being of degree zero?

asked 2021-08-23 13:44:18 +0100

start1133 gravatar image

updated 2021-08-23 14:42:59 +0100

In sage, using 'letterplace’ can get free algebra with homogenous degrees but the degree of the generators of the algebra have to be positive degree. Is there any code that I can get an algebra that allows generators of degree zero?

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slelievre gravatar imageslelievre ( 2021-08-23 13:51:34 +0100 )edit

I guess the simple reason for an implementation to allow only generators of positive degree is to ensure finite-dimensional graded components, so that many problems become amenable to computation. What exactly do you want to do with your algebra (which would have infinite-dimensional graded parts)?

rburing gravatar imagerburing ( 2021-08-24 18:05:28 +0100 )edit

Thanks for your reply. In fact, in my case, it is a differential grade algebra, which I would like to use sage to compute the cohomology. This dga has degree-zero generators, say x_i (finitely many), and some generators in degree one. The degree-zero generators satisfy x_i^2=x_i. So it is of finite type.

start1133 gravatar imagestart1133 ( 2021-08-25 06:16:59 +0100 )edit