Double-partition Quantum Cluster Algebras
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Standard
Double-partition Quantum Cluster Algebras. / Jakobsen, Hans Plesner; Zhang, Hechun.
I: Journal of Algebra, Bind 372, 2012, s. 172-203.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Double-partition Quantum Cluster Algebras
AU - Jakobsen, Hans Plesner
AU - Zhang, Hechun
PY - 2012
Y1 - 2012
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
VL - 372
SP - 172
EP - 203
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 44050463