How to define a noncommutative derivative

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SUMMARY

The discussion focuses on defining a derivative in noncommutative spaces, specifically referencing the k-Poincaré algebra where the commutation relations are given by [X_i, X_j] = θ_{ijk}X_k. Participants seek clarity on how traditional derivative definitions can be adapted to these mathematical structures. The conversation emphasizes the need for a robust framework to handle derivatives in noncommutative geometry.

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  • Understanding of noncommutative geometry
  • Familiarity with k-Poincaré algebra
  • Knowledge of traditional derivative definitions in calculus
  • Basic concepts of algebraic structures and commutation relations
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  • Research "noncommutative calculus" to explore derivative definitions in noncommutative spaces
  • Study "k-Poincaré algebra" for insights into its structure and applications
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luxxio
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first of all, i don't know if this is the correct place to post this topic, if no tell me.

My question is, i have a definition of derivative that can not be applied to a noncommutative space. How i can define a derivative in a noncommutative space?

thank you.
 
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What is an example of a "noncommutative space" where you wish to do this?
 
g_edgar said:
What is an example of a "noncommutative space" where you wish to do this?

k-poincarè... [X_i,X_j]=\theta_{ijk}X_k
 

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