THE BUBBLE ALGEBRAS AT ROOTS OF UNITY

Authors

  • Mufida M. Hmaida

DOI:

https://doi.org/10.65540/jar.v13i.923

Keywords:

Temperley-Lieb algebra, multi-colour partition algebras and bubble algebras.

Abstract

We introduce multi-colour partition algebras , then define the bubble algebra  as a sub-algebra of . We present general techniques to determine the structure of the bubble algebra over the complex field in the non-semisimple case.

References

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U. Grimm and P. Martin. The bubble algebra: structure of a two-colour Temperley-Lieb algebra. J. Physics, 36(42):10551-10571, 2003. DOI: https://doi.org/10.1088/0305-4470/36/42/010

M. Jegan. Homomorphisms between bubble algebra modules. PhD thesis, City University, 2013.

P. Martin. Potts models and related problems in statistical mechanics, volume 5. World Scientific, 1991. DOI: https://doi.org/10.1142/0983

P. Martin, R. Green and A. Parker, Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond, J. of Algebra, 316(1): 392-452, 2007. DOI: https://doi.org/10.1016/j.jalgebra.2007.04.013

D. Ridout and Y. Saint. Standard modules, induction and the structure of the Temperley-Lieb algebra. Advances in Theoretical and Mathematical Physics, 18(5):957-1041, 2014. DOI: https://doi.org/10.4310/ATMP.2014.v18.n5.a1

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Published

2019-01-30

How to Cite

Hmaida, M. M. (2019). THE BUBBLE ALGEBRAS AT ROOTS OF UNITY. Journal of Academic Research, 13, 15–26. https://doi.org/10.65540/jar.v13i.923

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