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The quantic monoid and degenerate quantized enveloping algebras

Markus Reineke
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Abstract

We study a monoid associated to complex semisimple Lie algebras, called the quantic monoid. Its monoid ring is shown to be isomorphic to a degenerate quantized enveloping algebra. Moreover, we provide normal forms and a straightening algorithm for this monoid. All these results are proved by a realization in terms of representations of quivers, namely as the monoid of generic extensions of a quiver with automorphism.

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Markus Reineke. 2002-06-10. The quantic monoid and degenerate quantized enveloping algebras. https://arxiv.org/abs/math/0206095

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