Abstract:<abstract><p>Associated with a reductive algebraic group $ G $ and its rational representation $ (\rho, M) $ over an algebraically closed filed $ {\bf{k}} $, the authors define the enhanced reductive algebraic group $ {\underline{G}}: = G\ltimes_\rho M $, which is a product variety $ G\times M $ and endowed with an enhanced cross product in <sup>[<xref ref-type="bibr" rid="b5">5</xref>]</sup>. If $ {\underline{G}} = GL(V)\ltimes_{\eta} V $ with the natural representation $ (… Show more
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