Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple. 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

References in zbMATH (referenced in 13 articles )

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  1. Hitzer, Eckhard: General steerable two-sided Clifford Fourier transform, convolution and mustard convolution (2017)
  2. Prodanov, D.; Toth, V.T.: Sparse representations of Clifford and tensor algebras in maxima (2017)
  3. Castro, Carlos: Moyal deformations of Clifford gauge theories of gravity (2016)
  4. Abłamowicz, Rafał; Fauser, Bertfried: Using periodicity theorems for computations in higher dimensional Clifford algebras (2014)
  5. Abłamowicz, Rafał; Fauser, Bertfried: On parallelizing the Clifford algebra product for CLIFFORD (2014)
  6. Hitzer, Eckhard: Two-sided Clifford Fourier transform with two square roots of $-1$ in $Cl(p,q)$ (2014)
  7. Hitzer, Eckhard; Helmstetter, Jacques; Abłamowicz, Rafał: Square roots of $-1$ in real Clifford algebras (2013)
  8. Abłamowicz, Rafał; Fauser, Bertfried: On the transposition anti-involution in real Clifford algebras. III: The automorphism group of the transposition scalar product on spinor spaces (2012)
  9. Hitzer, Eckhard; Abłamowicz, Rafał: Geometric roots of $-1$ in Clifford algebras $C \ell_p,q$ with $p + q \leq 4$ (2011)
  10. Bangoura, Momo: Homotopy Lie algebra associated to a proto-Lie bigebra (2007)
  11. Fauser, Bertfried: Products, coproducts, and singular value decomposition (2006)
  12. Abłamowicz, Rafał; Fauser, Bertfried: Clifford and Gra\ssmannHopf algebras via the BIGEBRA package for Maple (2005)
  13. Gerritzen, L.: On Hopf algebras related to triangular matrices (1994)