Generalised Magnus Modules over the Braid Group
نویسنده
چکیده
W. Magnus’ representations of submonoids E ≤ End(F ) of the endomorphisms of a free group F of finite rank are generalised by identifying them with the first homology group of F with particular coefficient modules. By considering a suitable free resolution of the integers over the semidirect product of free groups, a class of representations of the braid group can be obtained on higher homology groups. The resolution shows that the holonomy representations of the braid group and of the Hecke algebra constructed topologically by R. J. Lawrence belong to this class.
منابع مشابه
A Cellular Braid Action and the Yang - Baxterequationmirko L
Using a theorem of Schechtman-Varchenko on integral expressions for solutions of Knizhnik-Zamolodchikov equations we prove that the solutions of the Yang-Baxter equation associated to complex simple Lie algebras belong to the class of generalised Magnus representations of the braid group. Hence they can be obtained from the homology of a certain cell complex , or equivalently as group homology ...
متن کاملA Cellular Braid Action and the Yang - Baxter Equation
Using a theorem of Schechtman Varchenko on integral expressions for solutions of Knizhnik Zamolodchikov equations we prove that the solutions of the Yang Baxter equation associated to complex simple Lie algebras belong to the class of generalised Magnus representations of the braid group. Hence they can be obtained from the homology of a certain cell complex, or equivalently as group homology o...
متن کاملGeneralizations of the standard Artin representation are unitary
We consider the Magnus representation of the image of the braid group under the generalizations of the standard Artin representation discovered by M. Wada. We show that the images of the generators of the braid group under the Magnus representation are unitary relative to a Hermitian matrix. As a special case, we get that the Burau representation is unitary, which was known and proved by C. C. ...
متن کاملBraids and crossed modules
For n ≥ 4, we describe Artin’s braid group on n strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations. Subject classification: Primary: 20F36 57M05 57M20 57M25; Secondary: 18D50 18G55 20C08 55P48
متن کاملFree Groups and Finite Type Invariants of Pure Braids
In this paper finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal invariant with integer coefficients based on the Magnus expansion of a free group and a calculation of numbers of independent invariants of each type for all pure braid groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995