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Added by Arxiv Bot | Added: 2026-03-02 18:01 | Views: 1 | Source: arXiv Dataset IDs (Model)

On some quadratic algebras

Authors	Anatol N. Kirillov
Categories	q-alg math.QA
ArXiv ID	q-alg/9705003
URL	https://arxiv.org/abs/q-alg/9705003

Abstract

We study some quadratic algebras which are appeared in the low-dimensional topology and Schubert calculus. We introduce the Jucys-Murphy elements in the braid algebra and in the pure braid group, as well as the Dunkl elements in the extended affine braid group. Relationships between the Dunkl elements, Dunkl operators and Jucys-Murphy elements are described.

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    "abstract": "We study some quadratic algebras which are appeared in the low-dimensional\ntopology and Schubert calculus. We introduce the Jucys-Murphy elements in the\nbraid algebra and in the pure braid group, as well as the Dunkl elements in the\nextended affine braid group. Relationships between the Dunkl elements, Dunkl\noperators and Jucys-Murphy elements are described.",
    "arxiv_id": "q-alg/9705003",
    "authors": [
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    "title": "On some quadratic algebras",
    "url": "https://arxiv.org/abs/q-alg/9705003"
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