THE BUBBLE ALGEBRAS AT ROOTS OF UNITY

Authors

  • Mufida M. Hmaida

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.

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.

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.

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.

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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. Retrieved from https://lam-journal.ly/index.php/jar/article/view/923

Issue

Vol. 13 (2019)

Section

Article

License

Copyright (c) 2019 Mufida M. Hmaida

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.