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Mohamed Imad Bakhira and
Benjamin Cooper
Gradation of Algebras of Curves by the Winding Number
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| Published: |
September 13, 2018 |
| Keywords: |
Goldman Lie algebra, winding number, HOMFLY-PT skein, grading. |
| Subject: |
16T99, 53D99, 81R50. |
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Abstract
We construct a new grading on the Goldman Lie algebra of a closed oriented
surface by the winding number. This grading induces a grading on the
HOMFLY-PT skein algebra and related algebras. Our work supports the conjectures of B. Cooper and P. Samuelson in their paper "The Hall algebras of surfaces I".
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| Acknowledgements
The second author would like to thank P. Samuelson for the friendly conversations and suggestions. Both authors would like to thank C. Frohman and J. Greene, as well as the referee for the careful reading.
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| Author information
Mohamed Imad Bakhira:
Department of Mathematics,University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA.
mohamedimad-bakhira@uiowa.edu
Benjamin Cooper:
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA.
ben-cooper@uiowa.edu
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