Clifford and Grassmann Hopf algebras via the BIGEBRA package for Maple

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 [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.

arXiv comment18 pages, homepage of BIGEBRA : http://math.tntech.edu/rafal/

References in corpus (5)

• On the Hopf algebraic origin of Wick normal-ordering
• Quantum field theory and Hopf algebra cohomology
• Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras
• A Treatise on Quantum Clifford Algebras
• Clifford Hopf gebra for two-dimensional space

Cited by in corpus (6)

• New branching rules induced by plethysm
• Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras
• Sparse Representations of Clifford and Tensor algebras in Maxima
• Formalizing Geometric Algebra in Lean
• The Dirichlet Hopf algebra of arithmetics
• Clifford Algebras, Multipartite Systems and Gauge Theory Gravity