EXTRASPECIAL 2-GROUPS AND IMAGES OF BRAID GROUP REPRESENTATIONS
نویسندگان
چکیده
منابع مشابه
Extraspecial 2-groups and Images of Braid Group Representations
We investigate a family of (reducible) representations of the braid groups Bn corresponding to a specific solution to the YangBaxter equation. The images of Bn under these representations are finite groups, and we identify them precisely as extensions of extraspecial 2-groups. The decompositions of the representations into their irreducible constituents are determined, which allows us to relate...
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In this paper we survey some work on representations of Bn given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representation, recently came to prominence when it was shown to be faithful for all n. We will outline the methods used, applying them to a closely related representation for which the proof is slightly easier. The main tool is the...
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To understand what a braid group is, it is easiest to visualize a braid. Consider n strands, all parallel. Consider taking the ith strand and crossing it over the very next strand. This is a braid. In fact, a braid is any sequence of crossings of the bands, provided none of the bands are self-crossing. For instance, a loop, or a band which forms a loop in the middle are not braids. Now, in orde...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2006
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216506004580