The non-Abelian momentum map for Poisson-Lie symmetries on the chiral WZNW phase space

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dc.creatorFeher, L.
dc.creatorMarshall, I.
dc.date2004-01-19
dc.date2004-04-05
dc.date.accessioned2026-07-07T05:04:39Z
dc.date.available2026-07-07T05:04:39Z
dc.descriptionThe gauge action of the Lie group $G$ on the chiral WZNW phase space ${\cal M}_{\check G}$ of quasiperiodic fields with $\check G$-valued monodromy, where $\check G\subset G$ is an open submanifold, is known to be a Poisson-Lie (PL) action with respect to any coboundary PL structure on $G$, if the Poisson bracket on ${\cal M}_{\check G}$ is defined by a suitable monodromy dependent exchange $r$-matrix. We describe the momentum map for these symmetries when $G$ is either a factorisable PL group or a compact simple Lie group with its standard PL structure. The main result is an explicit one-to-one correspondence between the monodromy variable $M \in \check G$ and a conventional variable $Ω\in G^*$. This permits us to convert the PL groupoid associated with a WZNW exchange $r$-matrix into a `canonical' PL groupoid constructed from the Heisenberg double of $G$, and consequently to obtain a natural PL generalization of the classical dynamical Yang-Baxter equation.
dc.description22 pages, v2: with clarifying remarks added in the introduction
dc.identifierhttps://arxiv.org/abs/math/0401226
dc.identifierhttp://arxiv.org/abs/math/0401226
dc.identifierInt. Math. Res. Not. 2004, no. 49, 2611-2636
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69887
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject37J15, 53D17, 17Bxx, 81T40
dc.titleThe non-Abelian momentum map for Poisson-Lie symmetries on the chiral WZNW phase space
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