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Cluster superalgebras

Authors
  • Ovsienko, Valentin
Type
Preprint
Publication Date
Mar 24, 2015
Submission Date
Mar 06, 2015
Identifiers
arXiv ID: 1503.01894
Source
arXiv
License
Yellow
External links

Abstract

We introduce cluster superalgebras, a class of ${\mathbb Z}_2$-graded commutative algebras generalizing cluster algebras of Fomin and Zelevinsky. These algebras contain odd coordinates that anticommute with each other and square to zero. A cluster superalgebra is defined with the help of a quiver satisfying some conditions and specific transformations called mutations. Generators of a cluster superalgebra are Laurent polynomials with denominators given by even monomials. Both, mutations and exchange relations, generalize the classical ones. Every cluster superalgebra admits a presymplectic form invariant under mutations. Our main series of examples of cluster superalgebras is provided by superfriezes~arXiv:1501.07476, analogous to Coxeter's frieze patterns.

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