On the transposition anti-involution in real Clifford algebras I: the transposition map

DOI10.1080/03081087.2010.517201zbMath1393.15029arXiv1005.3554OpenAlexW2022359942MaRDI QIDQ3104563

Bertfried Fauser, Rafał Abłamowicz

Publication date: 14 December 2011

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3554

zbMATH Keywords

correlationcontractionquadratic formdual spaceinvolutionconjugationexterior algebraindecomposable modulemonomial orderprimitive idempotentleft regular representationreversionsimple algebragraded tensor productminimal left idealgrade involutionspinor modulestranspose of linear mapping

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Clifford algebras, spinors (15A66) Quadratic spaces; Clifford algebras (11E88)

Related Items (16)

Method of averaging in Clifford algebras ⋮ Lie algebra of unit tangent bundle ⋮ Involutions in dual split-quaternions ⋮ A classification of Clifford algebras as images of group algebras of Salingaros vee groups ⋮ Unnamed Item ⋮ The inverse of a multivector: beyond the threshold \(p+q=5\) ⋮ Classification of Lie algebras of specific type in complexified Clifford algebras ⋮ The Moore-Penrose inverse and singular value decomposition of split quaternions ⋮ A new view of generalized Clifford algebras ⋮ Unnamed Item ⋮ Heisenberg's and Hardy's uncertainty principles for special relativistic space-time Fourier transformation ⋮ 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 II: stabilizer groups of primitive idempotents ⋮ A note on the representation of Clifford algebras ⋮ \(CPT\) groups of spinor fields in de Sitter and anti-de Sitter spaces

Uses Software

• CLIFFORD
• GfG

Cites Work

• Computation of non-commutative Gröbner bases in Grassmann and Clifford algebras
• Positronium as an example of algebraic composite calculations
• Products, coproducts, and singular value decomposition
• Monoïdes de Clifford et déformations d'algèbres de Clifford. (Clifford monoids and deformations of Clifford algebras)
• Combinatorial aspects of the \(K\)-theory of Grassmannians
• Universal coverings of orthogonal groups.
• Computations with Clifford and Grassmann algebras
• On the Hopf algebraic origin of Wick normal ordering
• Clifford geometric parameterization of inequivalent vacua
• Operator Homology and Cohomology in Clifford Algebras
• On the transposition anti-involution in real Clifford algebras II: stabilizer groups of primitive idempotents
• The relationship between finite groups and Clifford algebras
• Realization, extension, and classification of certain physically important groups and algebras
• Hecke algebra representations within Clifford geometric algebras of multivectors
• Plethystic Hopf algebras.

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