عنوان

The Gassner representation of the pure braid group

شماره

TLpq304203806

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

The Gassner representation of the pure braid group

نام عام مواد

[Thesis]

نام نخستين پديدآور

M. N. Adbulrahim

نام ساير پديدآوران

E. Formanek

نام ناشر، پخش کننده و غيره

The Pennsylvania State University

تاریخ نشرو بخش و غیره

1995

نام خاص و کميت اثر

60

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

The Pennsylvania State University

امتياز متن

1995

متن يادداشت

The braid group usdB\sb{n}usd has a lot of geometric meaning. However, I will treat usdB\sb{n}usd as an abstract group with generators and relations. usdB\sb{n}usd has a normal subgroup of index n!; this latter subgroup is called the pure braid group and is denoted by usdP\sb{n}.usd The first part of my work will be centered on the Burau representation of usdB\sb{n}usd and the Gassner representation of usdP\sb{n}.usd I will show that the Gassner representation of usdP\sb{n}usd of degree n is reducible to a representation of degree usdn-1usd, called the reduced Gassner representation, and the images of the generators of usdP\sb{n}usd under this representation are pseudoreflections. Next I will prove a necessary and sufficient condition for a specialization of the reduced Gassner representation to be irreducible in usdGL\sb{n-1}(\rm C).usd The second part of my work will be directed towards the open question of whether the reduced Gassner representation of usdP\sb{n}usd is faithful or not. It is known that for usdn \ge 6,usd the Burau representation of usdB\sb{n}usd is not faithful. I will prove two theorems which might help us to approach that open question about the faithfulness of the reduced Gassner representation of usdP\sb{n}.usd The first one shows that the image of the reduced Gassner representation consists of unitaries relative to an explicit Hermitian form. This provides a tool for attacking the question of whether or not the Gassner representation is faithful. This leads us to the second theorem which provides us with a necessary and a sufficient condition for an element of usdP\sb{n}usd to be in the kernel of the reduced Gassner representation.

موضوع مستند نشده

braid group

موضوع مستند نشده

Burau representation

موضوع مستند نشده

Mathematics

موضوع مستند نشده

Pure sciences

مستند نام اشخاص تاييد نشده

E. Formanek

مستند نام اشخاص تاييد نشده

M. N. Adbulrahim

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y