##  [Gelfand–Kirillov Dimension](/gelfand-kirillov-dimension) 

  ##  [Gelfand–Kirillov Dimension](https://algebra.quantumdictionary.io/gelfand-kirillov-dimension-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A growth invariant of a finitely generated algebra A over a field that measures the asymptotic rate of growth of dimensions of powers of a finite-dimensional generating subspace V, typically defined by GKdim(A)=limsup_{n→∞} log(dim V^n)/log n.