On the transposition anti-involution in real Clifford algebras III: the automorphism group of the transposition scalar product on spinor spaces

DOI10.1080/03081087.2011.624093zbMath1388.15021arXiv1102.3304OpenAlexW2080980639MaRDI QIDQ2895705

Rafał Abłamowicz, Bertfried Fauser

Publication date: 4 July 2012

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

Full work available at URL: https://arxiv.org/abs/1102.3304

zbMATH Keywords

spinortransversalinvolutionsemisimple algebragroup ringstabilizerindecomposable modulemonomial orderprimitive idempotentreversiontwisted group ringminimal left idealuniversal Clifford algebragrade involution

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Clifford algebras, spinors (15A66) Twisted and skew group rings, crossed products (16S35)

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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 ⋮ 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 ⋮ On inner automorphisms preserving fixed subspaces of Clifford algebras ⋮ 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

Uses Software

• BIGEBRA
• CLIFFORD
• Maple

Cites Work

• Unnamed Item
• Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple
• Simple graded commutative algebras.
• Clifford algebras obtained by twisting of group algebras
• Mathematics of Clifford -- a Maple package for Clifford and Graßmann algebras
• Computations with Clifford and Grassmann algebras
• The relationship between finite groups and Clifford algebras
• Realization, extension, and classification of certain physically important groups and algebras
• On the classification of Clifford algebras and their relation to spinors in n dimensions