Double-partition Quantum Cluster Algebras

Hans Plesner Jakobsen; Hechun Zhang

doi:10.1016/j.jalgebra.2012.09.015

Double-partition Quantum Cluster Algebras

Hans Plesner Jakobsen, Hechun Zhang

Department of Mathematical Sciences

2 Citations (Scopus)

Abstract

A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti-
tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to
another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis.

Original language	English
Journal	Journal of Algebra
Volume	372
Pages (from-to)	172-203
ISSN	0021-8693
DOIs	https://doi.org/10.1016/j.jalgebra.2012.09.015
Publication status	Published - 5 Dec 2012

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10.1016/j.jalgebra.2012.09.015

Cite this

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title = "Double-partition Quantum Cluster Algebras",

abstract = "A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis.",

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AU - Jakobsen, Hans Plesner

AU - Zhang, Hechun

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N2 - A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis.

AB - A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis.

U2 - 10.1016/j.jalgebra.2012.09.015

DO - 10.1016/j.jalgebra.2012.09.015

M3 - Journal article

SN - 0021-8693

VL - 372

SP - 172

EP - 203

JO - Journal of Algebra

JF - Journal of Algebra

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