This work constructs generalized Burau representations in braid groups, highlighting connections to Iwahori–Hecke and Temperley–Lieb algebras.
In this paper, we construct generalized Burau representations of virtual and welded braid groups. For the Gassner representation, this paper gives a machinery for constructing new welded pure braid representations, and it allows to recover and generalize the extended classical Gassner representation. In addition, we introduce the virtual Iwahori–Hecke algebra with two parameters defined as an extension of the classical Iwahori–Hecke algebra and we observe that it has a connection with the virtual Temperley–Lieb algebra given by Paris and Rabenda.
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Abdoulrahim Ibrahim (2025) studied this question.
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