Leavitt Path Algebras, $B_{\infty }$-Algebras and Keller's Conjecture for Singular Hochschild Cohomology (Memoirs of the American Mathematical Society)

Chen, Xiao-Wu/ Li, Huanhuan/ Wang, Zhengfang

American Mathematical Society（2025/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 116 p.
• 言語 ENG
• 商品コード 9781470476168

Full Description

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.

Contents

1. Introduction
2. DG categories and dg quotients
3. The dg singularity category and acyclic complexes
4. Quivers and Leavitt path algebras
5. An introduction to $B_\infty $-algebras
6. The Hochschild cochain complexes
7. A homotopy deformation retract and the homotopy transfer theorem
8. The singular Hochschild cochain complexes
9. $B_\infty $-quasi-isomorphisms induced by one-point (co)extensions and bimodules
10. Algebras with radical square zero and the combinatorial $B_\infty $-algebra
11. The Leavitt $B_{\infty }$-algebra as an intermediate object
12. An $A_\infty $-quasi-isomorphism for the Leavitt path algebra
13. Verifying the $B_\infty $-morphism
14. Keller's conjecture and the main results