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Cyclic Pairings and Noncommutative Poisson Structures
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Cyclic Pairings and Noncommutative Poisson Structures. |
| 개인저자 | Zhang, Yining. |
| 단체저자명 | Indiana University. Mathematics. |
| 발행사항 | [S.l.]: Indiana University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 132 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088351987 |
| 학위논문주기 | Thesis (Ph.D.)--Indiana University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Ramadoss, Ajay C. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | By a fundamental theorem of Quillen, there is a natural duality - an instance of general Koszul duality - between differential graded (DG) Lie algebras and DG cocommutative coalgebras defined over a field $k$ of characteristic $0$. A cyclic pairing (i.e., an inner product satisfying a natural cyclicity condition) on the cocommutative coalgebra gives rise to an interesting structure on the universal enveloping algebra $\\mathcal{U}\\mathfrak{a}$ of the Koszul dual Lie algebra $\\mathfrak{a}$ called the derived Poisson bracket. We study the general properties of cyclic pairings on DG coalgebras and DG Lie coalgebras. We also study the derived Poisson brackets on universal enveloping algebras $\\mathcal{U}\\mathfrak{a}$, and their relation to the classical Poisson brackets on the derived moduli spaces $\\mathrm{DRep}_\\mathfrak{g}(\\mathfrak{a})$ of representations of $\\mathfrak{a}$ in a finite dimensional semisimple Lie algebra $\\mathfrak{g}$. More specifically, we show that certain derived character maps of $\\mathfrak{a}$ intertwine the derived Poisson bracket with the classical Poisson structure on the representation homology $\\mathrm{HR}_\\bullet(\\mathfrak{a},\\,\\mathfrak{g})$ related to $\\mathrm{DRep}_\\mathfrak{g}(\\mathfrak{a})$. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
