Computations with Clifford and Grassmann algebras

DOI10.1007/s00006-009-0182-3zbMath1182.65068OpenAlexW2001005800MaRDI QIDQ2655363

Rafał Abłamowicz

Publication date: 25 January 2010

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00006-009-0182-3

zbMATH Keywords

contractionsingular value decompositionspinorsalgebraic equationsquaternionsHopf algebraquantum Clifford algebraminimal polynomialconformal groupoctonionswedge productGrassmann algebrareversionmultivectorgrade involutionVahlen matrixdotted wedge productMaple package \texttt{CLIFFORD}

Mathematics Subject Classification ID

Related Items (14)

Lie algebra of unit tangent bundle ⋮ On the transposition anti-involution in real Clifford algebras III: the automorphism group of the transposition scalar product on spinor spaces ⋮ Involutions in dual split-quaternions ⋮ The modified Pell and the modified \(k\)-Pell quaternions and octonions ⋮ Algebraic foundations of split hypercomplex nonlinear adaptive filtering ⋮ An extended implementation framework for geometric algebra operations on systems of coordinate frames of arbitrary signature ⋮ Unnamed Item ⋮ Embedding of octonion Fourier transform in geometric algebra of \(\mathbb{R}^3\) and polar representations of octonion analytic signals ⋮ General steerable two-sided Clifford Fourier transform, convolution and mustard convolution ⋮ Two-sided Clifford Fourier transform with two square roots of \(-1\) in \(Cl(p,q)\) ⋮ On parallelizing the Clifford algebra product for \texttt{CLIFFORD} ⋮ Using periodicity theorems for computations in higher dimensional Clifford algebras ⋮ On the transposition anti-involution in real Clifford algebras I: the transposition map ⋮ On hyperholomorphic $F^{\alpha}_{\omega,G}(p,q,s)$ spaces of quaternion valued functions

Uses Software

• AXIOM
• BIGEBRA
• CLIFFORD
• CoCoA
• Macaulay2
• Maple
• SINGULAR
• CLICAL

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