• Corpus ID: 119279206

A step towards cluster superalgebras

@article{Ovsienko2015AST,
  title={A step towards cluster superalgebras},
  author={Valentin Ovsienko},
  journal={arXiv: Combinatorics},
  year={2015}
}
  • V. Ovsienko
  • Published 6 March 2015
  • Mathematics
  • arXiv: Combinatorics
We introduce a class of commutative superalgebras generalizing cluster algebras. A cluster superalgebra is defined by a hypergraph called an "extended quiver", and transformations called mutations. We prove the super analog of the "Laurent phenomenon", i.e., that all elements of a given cluster superalgebra are Laurent polynomials in the initial variables, and find an invariant presymplectic form. Examples of cluster superalgebras are provided by superanalogs of Coxeter's frieze patterns. We… 
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40 References

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