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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Arc diagrams · PBWDeformations.jl</title><script data-outdated-warner src="../assets/warner.js"></script><link rel="canonical" href="https://lgoettgens.github.io/PBWDeformations.jl/arc_diagrams/"/><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link 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id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">PBWDeformations.jl</a></li><li><a class="tocitem" href="../smash_product_lie/">Smash products</a></li><li><a class="tocitem" href="../smash_product_deform_lie/">Smash product deformations</a></li><li><a class="tocitem" href="../smash_product_pbwdeform_lie/">PBWDeformations</a></li><li class="is-active"><a class="tocitem" href>Arc diagrams</a><ul class="internal"><li><a class="tocitem" href="#Arc-diagram-induced-bases"><span>Arc diagram induced bases</span></a></li><li><a class="tocitem" href="#Reverse-direction"><span>Reverse direction</span></a></li></ul></li><li><a class="tocitem" href="../pseudographs/">Pseudographs</a></li><li><a class="tocitem" href="../util/">Util functions</a></li><li><a class="tocitem" href="../references/">References</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Arc diagrams</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Arc diagrams</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/lgoettgens/PBWDeformations.jl/blob/master/docs/src/arc_diagrams.md#" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Arc-diagrams"><a class="docs-heading-anchor" href="#Arc-diagrams">Arc diagrams</a><a id="Arc-diagrams-1"></a><a class="docs-heading-anchor-permalink" href="#Arc-diagrams" title="Permalink"></a></h1><h2 id="Arc-diagram-induced-bases"><a class="docs-heading-anchor" href="#Arc-diagram-induced-bases">Arc diagram induced bases</a><a id="Arc-diagram-induced-bases-1"></a><a class="docs-heading-anchor-permalink" href="#Arc-diagram-induced-bases" title="Permalink"></a></h2><div class="admonition is-warning"><header class="admonition-header">Warning</header><div class="admonition-body"><p>The basis <a href="#PBWDeformations.ArcDiagDeformBasis"><code>ArcDiagDeformBasis</code></a> can currently only be used for exterior and symmetric powers of the standard module of special orthogonal Lie algebras.</p></div></div><article class="docstring"><header><a class="docstring-binding" id="PBWDeformations.ArcDiagDeformBasis" href="#PBWDeformations.ArcDiagDeformBasis"><code>PBWDeformations.ArcDiagDeformBasis</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Concrete subtype of <a href="../smash_product_pbwdeform_lie/#PBWDeformations.DeformBasis"><code>DeformBasis</code></a>. Each element of the basis is induced by an arc diagram of a suitable size, which gets symmetrized and specialised to the given smash product. This process is due to <a href="../references/#FM22">[FM22]</a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lgoettgens/PBWDeformations.jl/blob/71fc33edfadd9914e31b802bc14a21d82a4c4c5d/src/DeformationBases/ArcDiagDeformBasis.jl#L4-L9">source</a></section></article><h2 id="Reverse-direction"><a class="docs-heading-anchor" href="#Reverse-direction">Reverse direction</a><a id="Reverse-direction-1"></a><a class="docs-heading-anchor-permalink" href="#Reverse-direction" title="Permalink"></a></h2><p>Given a basis element of an above basis, one can lookup all arc diagrams that induce it (up to a scalar).</p><article class="docstring"><header><a class="docstring-binding" id="PBWDeformations.lookup_data" href="#PBWDeformations.lookup_data"><code>PBWDeformations.lookup_data</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">lookup_data(m::DeformationMap{C}, basis::DeformBasis{C}) where {C &lt;: RingElem}</code></pre><p>Look up additional data that was used to generate the deformation map <code>m</code> in the basis <code>basis</code>. This can e.g. be an arc diagram or a pseudograph.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/lgoettgens/PBWDeformations.jl/blob/71fc33edfadd9914e31b802bc14a21d82a4c4c5d/src/DeformationBases/DeformBasis.jl#L28-L33">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../smash_product_pbwdeform_lie/">« PBWDeformations</a><a class="docs-footer-nextpage" href="../pseudographs/">Pseudographs »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 12 June 2024 09:52">Wednesday 12 June 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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