Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple

Details Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple

2002-12-10

arxiv.org/abs/math-ph/0212032v1

Computer Physics Communications 170 (2005) 115-130

Physics

Mathematical Physics

18 pages, homepage of BIGEBRA : http://math.tntech.edu/rafal/

Scientific paper

10.1016/j.cpc.2005.04.001

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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