Gelfand–Kirillov dimension

In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module M over a k-algebra A is: GKdim = sup V , M 0 lim sup n → ∞ log n ⁡ dim k ⁡ M 0 V n {\displaystyle \operatorname {GKdim} =\sup _{V,M_{0}}\limsup _{n\to \infty }\log _{n}\dim _{k}M_{0}V^{n}} where the supremum is taken over all finite-dimensional subspaces V ⊂ A {\displaystyle V\subset A} and M 0 ⊂ M {\displaystyle M_{0}\subset M} . An algebra is said to have polynomial growth if its Gelfand–Kirillov dimension is finite.

Source: Wikipedia — Gelfand–Kirillov dimension (CC BY-SA 4.0)

Gelfand–Kirillov dimension

In algebra, the Gelfand–Kirillov dimension (or GK dimension) of a right module M over a k-algebra A is: GKdim = sup V , M 0 lim sup n → ∞ log n ⁡ dim k ⁡ M 0 V n {\displaystyle \operatorname {GKdim} =\sup _{V,M_{0}}\limsup _{n\to \infty }\log _{n}\dim _{k}M_{0}V^{n}} where the supremum is taken over all finite-dimensional subspaces V ⊂ A {\displaystyle V\subset A} and M 0 ⊂ M {\displaystyle M_{0}\subset M} . An algebra is said to have polynomial growth if its Gelfand–Kirillov dimension is finite.

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Source: Wikipedia "Gelfand–Kirillov dimension" · CC BY-SA 4.0

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