Positive half of the Witt algebra acts on triply graded link homology
Mikhail Khovanov, Lev Rozansky
TL;DR
This paper demonstrates that the positive half of the Witt algebra can be extended to act on triply graded link homology, revealing a new algebraic symmetry in link invariants.
Contribution
It establishes the extension of the positive Witt algebra action to triply graded link homology, connecting Lie algebra symmetries with link invariants.
Findings
Witt algebra acts on polynomial algebra Q[x]
Extension of Witt algebra action to link homology
New algebraic symmetry in link invariants
Abstract
The positive half of the Witt algebra is the Lie algebra spanned by vector fields x^{m+1} d/dx acting as differentiations on the polynomial algebra Q[x] upon which the Soergel bimodule construction of triply graded link homology is based. We show that this action of Witt algebra can be extended to the link homology.
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