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Decomposable braids as subgroups of braid groups
Transactions of the American Mathematical Society, 1975The group of all decomposable 3 3 -braids is the commutator subgroup of the group I 3 {I_3} of all 3 3 -braids which leave strand positions invariant. The group of all 2 2 -decomposable 4 4 -braids is the commutator subgroup of
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Braided Coadditive Differential Complexes on Quantized Braided Groups
International Journal of Theoretical Physics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, Yajun, Gui, Yuan-Xing
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Braided Covariance of the Braided Differential Bialgebras Under Quantized Braided Groups
International Journal of Theoretical Physics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gao, Yajun, Gui, Yuanxing
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Algebra and Logic, 2003
\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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1974
The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel planes in euclidean 3-space which we call respectively the upper and the lower frame. We choose n distinct points U v (v = 1, ..., n) in the upper frame and denote their orthogonal projections onto
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The terms “braid” and “braid groups” were coined by Artin, 1925. In his paper, an n-braid appears as a specific topological object. We consider two parallel planes in euclidean 3-space which we call respectively the upper and the lower frame. We choose n distinct points U v (v = 1, ..., n) in the upper frame and denote their orthogonal projections onto
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The Annals of Mathematics, 1947
In his paper 'Theorie der Z6pfe' E. Artin' presented a theory of braids based on a study of their projections on a two-dimensional plane. In the projection each strand of a braid appears as a line, vertical in general, but at certain levels two neighboring strands interchange position, one strand crossing in front of the other one.
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In his paper 'Theorie der Z6pfe' E. Artin' presented a theory of braids based on a study of their projections on a two-dimensional plane. In the projection each strand of a braid appears as a line, vertical in general, but at certain levels two neighboring strands interchange position, one strand crossing in front of the other one.
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DIAGRAM GROUPS, BRAID GROUPS, AND ORDERABILITY
Journal of Knot Theory and Its Ramifications, 2003We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.
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1999
In trying to establish a theory of braids, the most primitive question we may ask is, How many different (non-equivalent) braids are there?
Kunio Murasugi, Bohdan I. Kurpita
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In trying to establish a theory of braids, the most primitive question we may ask is, How many different (non-equivalent) braids are there?
Kunio Murasugi, Bohdan I. Kurpita
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International Journal of Theoretical Physics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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