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Trace polynomials of words in the free group of rank two
계수 2 자유군에서의 대각합 다항식

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Authors
박현수
Advisor
임선희
Issue Date
2020
Publisher
서울대학교 대학원
Keywords
Trace polynomialFree group of rank twoSpecial linear group,Cyclically reduced words대각합 다항식계수2 자유군특수 선형군순환 기약 워드
Description
학위논문 (석사) -- 서울대학교 대학원 : 자연과학대학 수리과학부, 2020. 8. 임선희.
Abstract
Procesi's theorem guarantees that traces in a two generator subgroup of $\ssl$ are polynomials in traces of the generators. These polynomials are called trace polynomials and defined for words in the free group of rank two. Let $\cw$ denote the set of cyclically reduced words in $F_2$.
Improving Jorgensen's algorithm, we classify all words in $\cw$ with the word lengths less than nine via their trace polynomials. Then we check whether they are in $\sim$-equivalence defined from the operation Mirror, Left shift, and Inverse on $\cw$.
We prove that two words of the same trace polynomials are $\sim$-equivalent when the word lengths are less than nine.
We also show, by counterexamples, this result does not hold for the word lengths greater than eight. As a corollary, we verify Wang's conjecture for the word lengths less than nine.
Language
eng
URI
http://hdl.handle.net/10371/170699

http://dcollection.snu.ac.kr/common/orgView/000000161223
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Master's Degree_수리과학부)
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