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FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS

Nohra Hage 1
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We study rewriting properties of the column presentation of plactic monoid for any semisimple Lie algebra such as termination and confluence. Littelmann described this presentation using L-S paths generators. Thanks to the shapes of tableaux, we show that this presentation is finite and convergent. We obtain as a corollary that plactic monoids for any semisimple Lie algebra satisfy homological finiteness properties.
Keywords : Littelmann path model Plactic algebra standard tableau convergent presentations
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https://hal-ujm.archives-ouvertes.fr/ujm-01248274
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Submitted on : Thursday, December 24, 2015 - 1:38:14 PM
Last modification on : Wednesday, November 20, 2019 - 3:22:58 AM

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  • HAL Id : ujm-01248274, version 1
  • ARXIV : 1512.07813

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Nohra Hage. FINITE CONVERGENT PRESENTATIONS OF PLACTIC MONOIDS FOR SEMISIMPLE LIE ALGEBRAS. 2015. ⟨ujm-01248274⟩

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