Möbius Tramsformations and Clifford Algebras of Euclidean and Anti-Euclidean Spaces

Lounesto, Pertti; Springer, Arthur

doi:10.1007/978-94-009-2643-1_8

Cited by 9 publications

(3 citation statements)

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“…For the background material on Vahlen matrices and conformal transformations, see [15,31,33,34,38]. Procedure isVahlenmatrix determines if a given 2 × 2 Clifford matrix V ∈ Mat(2, C (Q)) is a Vahlen matrix and it returns true or false accordingly.…”

Section: Vahlen Matricesmentioning

confidence: 99%

Computations with Clifford and Grassmann Algebras

Abłamowicz

2009

AACA

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Abstract. Various computations in Grassmann and Clifford algebras can be performed with a Maple package CLIFFORD. It can solve algebraic equations when searching for general elements satisfying certain conditions, solve an eigenvalue problem for a Clifford number, and find its minimal polynomial. It can compute with quaternions, octonions, and matrices with entries in C (B) -the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. It uses standard (undotted) Grassmann basis in C (Q) but when the antisymmetric part of B is non zero, it can also compute in a dotted Grassmann basis. Some examples of computations are discussed. Mathematics Subject Classification (2000). 15A66, 68W30.

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Section: Vahlen Matricesmentioning

confidence: 99%

Computations with Clifford and Grassmann Algebras

Abłamowicz

2009

AACA

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“…For more details the reader is directed to [18]. For this approach to the compactification of Minkowski spacetime see also [19][20][21][22]…”

Section: The Physical Dimensionmentioning

confidence: 99%

Holography and the future tube

Gibbons¹

2000

Class. Quantum Grav.

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“…Although this is not the only means of representing conformal transformations using Clifford algebra, (5)(6)(7)(8) the conformal split representation permits a remarkably simple analytic description of the Euclidean distance function, and has interesting connections with hyperbolic geometry (see below). The purpose of this paper is to show how the classical work by Menger, Blumenthal, and Seidel on distance geometry can be interpreted in the context of this representation, and to consider its wider invariant theoretic consequences.…”

Section: H I S T O R I C a L Introductionmentioning

confidence: 99%