대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권3호
  • /
  • Pages.445-454
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  • 2010
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS

  • 발행 : 2010.05.01
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초록

The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $TL_n$. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual presentation of braid groups, and then give a simple geometric proof for Zinno's theorem, using the interpretation of simple elements as non-crossing partitions.

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참고문헌

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피인용 문헌

  1. Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra vol.25, pp.06, 2016, https://doi.org/10.1142/S0218216516500358
  2. Dual braid monoids, Mikado braids and positivity in Hecke algebras vol.285, pp.1-2, 2017, https://doi.org/10.1007/s00209-016-1704-z