通过Maple的BIGEBRA软件包实现Clifford和Grassmann Hopf代数
Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple
摘要：
霍普夫代数结构将取代群和群表示作为未来时代的主要范式。K-理论，上同调，纠缠，统计，表示类别，量化或扭曲结构以及不变理论的更多几何主题，例如，Grassmann-Cayley括号代数都是由Hopf代数框架所覆盖的。实验数学的新分支允许人们通过使用符号操作和计算机代数系统（CAS）的直接计算轻松地进入这些领域。我们讨论的问题时，解决了建设的BIGEBRA包Maple和CLIFFORD [见数学-ph/0212031]处理张量积，格拉斯曼和Clifford代数，余代数和Hopf代数。最近的研究结果表明，CAS的有用性调查新的和涉及的数学为我们提供了例子。展望了进一步的发展。
英文摘要：
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as more geometric topics of invariant theory, e.g., the Grassmann-Cayley bracket algebra are all covered by the Hopf algebraic framework. The new branch of 'experimental mathematics' allows one to easily enter these fields through direct calculations using symbolic manipulation and computer algebra system (CAS). We discuss problems which were solved when building the BIGEBRA package for Maple and CLIFFORD [see math-ph/0212031] to handle tensor products, Grassmann and Clifford algebras, coalgebras and Hopf algebras. Recent results showing the usefulness of CAS for investigating new and involved mathematics provide us with examples. An outlook on further developments is given.
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