Graduate Can anybody please explain in layman terms the super-vector spaces?

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SUMMARY

Super-vector spaces refer to a mathematical structure that combines elements of vector spaces with additional properties, typically involving a notion of graduation and multiplication. The term "Fibonacci categories" lacks a widely accepted definition, making it challenging to find resources or references. The discussion highlights the difficulty in locating credible sources for Fibonacci categories, while super-vector spaces are adequately covered in existing literature, such as the Wikipedia article on the subject.

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  • Basic knowledge of algebraic concepts
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  • Read the Wikipedia article on Super Vector Spaces
  • Research academic papers that define Fibonacci categories
  • Explore the implications of graduation in vector spaces
  • Study the relationship between algebraic structures and category theory
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Mathematicians, students of advanced algebra, and researchers interested in vector spaces and category theory will benefit from this discussion.

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Can anybody please explain in layman terms the super-vector spaces and Fibonacci categories?
 
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Anixx said:
Can anybody please explain in layman terms the super-vector spaces and Fibonacci categories?
Can you give us a reference where you have read this? Super usually refers to a graduation and involves a multiplication. Vector spaces don't have multiplications. I couldn't find the term Fibonacci category either.
 
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Anixx said:
Can anybody please explain in layman terms the super-vector spaces and Fibonacci categories?
Super vector spaces are easy to fine. I suppose you have already seen the wiki article
https://en.wikipedia.org/wiki/Super_vector_space

Fibonacci categories are more difficult to find, but there are papers that use them and define them.
 
Since the OP hasn't returned to clarify where he got the terms from, I will close this thread now. If there is new information please send a message to a mentor and we might consider a reopening.
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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