

Preprint 52/2004
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.