Quantum Algebras, coalgebras and Invariants of Knots, Links and 3-Manifolds

摘要本文作者将继续长期研究由各种代数结构产生的结、1-1缠结和3-流形的不变量。他这一阶段的工作重点是研究量子余代数和它们所决定的不变量。它们解释了有限维量子代数产生的不变量。共拟三角形Hopf代数是量子共代数的一个例子。霍普夫代数和量子群是当代物理学中重要的代数对象，在几何和拓扑问题中也有应用。结理论在研究分子结构方面得到了应用。

RADFORD, 98-02178 Abstract The proposer will continue his long term investigation into invariants of knots, 1-1 tangles and 3-manifolds which arise from various algebraic structures. The focus of this phase of his work is the study of quantum coalgebras and the invariants they determine. They account for the invariants which arise from finite dimensional quantum algebras. Coquasitriangular Hopf algebras are examples of quantum coalgebras. Hopf algebras and quantum groups are algebraic objects whose study is important in contemporary physics and also which have application to geometric and topological problems. Knot theory has seen applications in the studying molecular structure.