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研究生： 許智祐
Syu, Jhih-You
論文名稱： 微分階化餘代數上的霍赫希爾德上同調
Hochschild cohomology of differential graded coalgebras
指導教授： 廖軒毅
Liao, Hsuan-Yi
口試委員: 鄭志豪
Teh, Jyh-Haur
賴俊儒
Lai, Chun-Ju
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2024
畢業學年度： 112
語文別： 英文
論文頁數： 43
中文關鍵詞： 霍赫希爾德上同調 、微分階化餘代數 、微分階化代數 、微分階化李代數 、導子
外文關鍵詞： Hochschild cohomology, differential graded algebra, differential graded coalgebra, differential graded Lie algebra, derivations
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    • 在這篇論文裡，對於任何一個微分階化餘代數C，我們在他的霍赫希爾德上同調上構造了微分階化代數以及微分階化李代數的結構。並且我們調查了這個霍赫希爾德上同調跟餘代數C的位移代數C[-1]的張量代數T(C[-1])的導子空間的關係。

    In this thesis, we construct DG (i.e., differential graded) algebra structures and DG Lie algebra structures on the Hochschild cochain complexes of any DG coalgebra C. We investigate the relationship between the Hochschild cochain complexes of C and the space Der(T(C[−1])) of derivations of the tensor algebra T(C[−1]) of C[−1].

    Acknowledgements i Abstract (Chinese version) ii Abstract iii Introduction 1 Notations and conventions 4 1. Preliminaries 5 1.1. Graded vector spaces 5 1.2. Differential graded (co)algebras 6 1.3. Degree-shifting map 8 2. Hochschild cochain complexes of DG coalgebras and their cohomology 9 2.1. Hochschild cochain complex of graded coalgebras 10 2.2. Hochschild cochain complex of DG coalgebras 15 2.3. Hochschild cochain product-total complex and shifted Hochschild complexes 21 3. DG Lie structure induced by derivations 24 3.1. Derivations of graded algebras and their relation to DG Lie algebras 24 3.2. Derivations of tensor algebras 25 3.3. Shifted DG coalgebras 26 3.4. Relationship between Hochschild cochain complexes and derivations 29 3.5. Hochschild cochain complex as a DG Lie algebra 33 4. DG algebra structure on Hochschild cochain complexes 34 4.1. The DG algebra structure on Hochschild cochain complexes 34 4.2. The DG algebra structure on the shifted derivation space 39 4.3. Comparison 42 References 43

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