Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper shows that every Plactic algebra of finite rank admits a finite Gröbner-Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to construct a finite complete rewriting system for the corresponding Plactic monoid, which also yields the corollaries that Plactic monoids of finite rank have finite derivation type and satisfy the homological finiteness properties left and right FP. Also, answering a question of Zelmanov, we apply this rewriting system and other techniques to show that Plactic monoids of finite rank are biautomatic.

Original languageEnglish
Pages (from-to)37-53
Number of pages17
JournalJournal of Algebra
Volume423
DOIs
Publication statusPublished - 1 Feb 2015

Keywords

  • Automatic monoids
  • Complete rewriting system
  • Gröbner-Shirshov basis
  • Plactic algebra
  • Plactic monoid
  • Primary
  • Secondary
  • Young tableau

Fingerprint Dive into the research topics of 'Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids'. Together they form a unique fingerprint.

  • Cite this