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- W2898660379 abstract "In 1987, Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the HOMFLY-PT polynomial invariant. In 2018, Kim generalized a Conway algebra, which is an algebraic structure with two skein relations, which is called a generalized Conway algebra. In 2017, Joung, Kamada, Kawauchi and Lee constructed a polynomial invariant of oriented surface-links by using marked graph diagrams. In this paper, we will introduce generalizations [Formula: see text] and [Formula: see text] of a Conway algebra and a generalized Conway algebra, which are called a marked Conway algebra and a generalized marked Conway algebra, respectively. We will construct invariants valued in [Formula: see text] and [Formula: see text] for oriented marked graphs and oriented surface-links by applying binary operations to classical crossings and marked vertices via marked graph diagrams. The polynomial invariant of oriented surface-links is obtained from the invariant valued in the marked Conway algebra with additional conditions." @default.
- W2898660379 created "2018-11-09" @default.
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- W2898660379 date "2018-11-01" @default.
- W2898660379 modified "2023-10-18" @default.
- W2898660379 title "Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams" @default.
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- W2898660379 doi "https://doi.org/10.1142/s0218216518420142" @default.
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