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Representation theory of Hopf algebras
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<p>In <a href="/facts/Abstract_algebra/YNNE1CNz">abstract algebra</a>, a representation of a <a href="/facts/Hopf_algebra/3QF6g0tT">Hopf algebra</a> is a <a href="/facts/Algebra_representation/1MaaEjqH">representation</a> of its underlying <a href="/facts/Associative_algebra/DRfoF6KV">associative algebra</a>. That is, a representation of a Hopf algebra <i>H</i> over a field <i>K</i> is a <i>K</i>-<a href="/facts/Vector_space/M1pxMLx2">vector space</a> <i>V</i> with an <a href="/facts/Group_action_(mathematics)/Vh9VtUUw">action</a> <i>H</i> × <i>V</i> → <i>V</i> usually denoted by juxtaposition (that is, the image of (<i>h</i>, <i>v</i>) is written <i>hv</i>). The vector space <i>V</i> is called an <i>H</i>-module. </p>