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2004•Journal of Knot Theory and Its RamificationsRequires access

THE LINKS–GOULD INVARIANT OF CLOSED 3-BRAIDS

Atsushi Ishii

Open publisher page 11 citations

Abstract

In this paper, we study the Links–Gould invariant of closed 3-braids. We consider the algebra generated by the image of the 3-string braid group by the linear representation which yields the Links–Gould invariant. We find fundamental linear relations among natural generators of the algebra, and we obtain a basis of the algebra. The relations allow us to evaluate the invariant of closed 3-braids recursively. As an application we give a computer program to calculate the invariant for closed 3-braids.

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What this paper is about

In this paper, we study the Links–Gould invariant of closed 3-braids. We consider the algebra generated by the image of the 3-string braid group by the linear representation which yields the Links–Gould invariant. We find fundamental linear relations among natural generators of the algebra, and we obtain a basis of the algebra. The relations allow us to evaluate the invariant of closed 3-braids recursively. As an application we give a computer program to calculate the invariant for closed 3-braids.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the Links–Gould invariant of closed 3-braids. We consider the algebra generated by the image of the 3-string braid group by the linear representation which yields the Links–Gould invariant. We find fundamental linear relations among natural generators of the algebra, and we obtain a basis of the algebra. The relations allow us to evaluate the invariant of closed 3-braids recursively. As an application we give a computer program to calculate the invariant for closed 3-braids.

Key concepts: Braid, Invariant (physics), Mathematics, Braid group, Braid theory, Algebra over a field, Pure mathematics, Finite type invariant

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