Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple

Rafal Ablamowicz and Bertfried Fauser

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Submission date: 22. Aug. 2004
Pages: 23
published in: Computer physics communications, 170 (2005) 2, p. 115-130 
DOI number (of the published article): 10.1016/j.cpc.2005.04.001
Bibtex
MSC-Numbers: 16W30, 15A66
Keywords and phrases: hopf algebras, deformation theoy, biconvolutions
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Abstract:
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 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.