SO(9,1) Group and Examples of Analytic Functions

Burdı́k, Č.; Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; La, Volkova

doi:10.1088/1742-6596/1194/1/012016

Cited by 7 publications

(12 citation statements)

References 4 publications

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“…This section provides us with a generalization some of the results presented for the quaternionic case in [2,7,16] to the non-associative octonionic case on the one hand and to arbitrary dimensional paravector spaces in associative Clifford algebras on the other hand. As already pointed out in the introduction, this topic in the octonionic setting attracts in the recent time a lot of interest from physicists in the context of extensions of the standard model of particle physics and super gravity, see for instance [5,11,20]. It should also be clearly mentioned that there are substantial differences between the related octonionic function theories and function theories in Clifford algebras which is also a topic of recent interest, see for instance [13,14,15].…”

Section: Resultsmentioning

confidence: 94%

“…As already pointed out in the introduction, this topic in the octonionic setting attracted in the recent time a lot of interest from physicists in the context of extensions of the standard model of particle physics and super gravity, see for instance [5,12,21].…”

Section: Resultsmentioning

confidence: 99%

“…For convenience we recall from [5,10,13,20] that the octonions offer an elegant representation of the SO(9, 1)-Möbius transformations (which can be R. S. Kraußhar Adv. Appl.…”

Section: Discussionmentioning

confidence: 99%

“…For convenience we recall from [5,9,12,19] that the octonions offer an elegant representation of the SO(9, 1)-Möbius transformations (which can be mapped bijectively to the set of octonionic conformal maps in the sense of Gauss). These can be written in the form T (z) = (az+b)(cz+d) −1 with octonions a, b, c, d ∈ O satisfying additionally the so-called Manogue-Schrader conditions, see [9] for details.…”

Section: Discussionmentioning

confidence: 99%

“…This paper underlines once more the particularity of the octonionic case in the context of Cayley-Dickson algebras concerning symmetry theories. It currently seems that the octonions provide the most adequate algebra to study the arising symmetries of recent physical attempts of setting up unifying theories in connection with the standard model of particle physics and supergravity, see [5,12,21].…”

Section: Introductionmentioning

confidence: 99%

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Conformal Mappings Revisited in the Octonions and Clifford Algebras of Arbitrary Dimension

Kraußhar

2020

Adv. Appl. Clifford Algebras

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In this paper we revisit the concept of conformality in the sense of Gauss in the context of octonions and Clifford algebras. We extend a characterization of conformality in terms of a system of partial differential equations and differential forms using special orthonormal sets of continuous functions that have been used before in the particular quaternionic setting. The aim is to describe to which higher dimensional algebras this characterization can exactly be extended and under which circumstances. It turns out to be crucial that this characterization requires a domain of definition that lies in a subalgebra that has the norm composition property and that is either associative (Clifford algebra case) or at least alternative (octonionic case). The orthonormal frames are elements of the spin group Spin$$(n+1)$$ ( n + 1 ) . We round off by relating the nature of the orthonormal frames to the associated Möbius transformation which are related to SO(9, 1) in the octonionic case and to the Ahlfors–Vahlen group in the case of a Clifford algebra.

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Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 99%

“…For convenience we recall from [5,10,13,20] that the octonions offer an elegant representation of the SO(9, 1)-Möbius transformations (which can be R. S. Kraußhar Adv. Appl.…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conformal Mappings Revisited in the Octonions and Clifford Algebras of Arbitrary Dimension

Kraußhar

2020

Adv. Appl. Clifford Algebras

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Recent and new results on octonionic Bergman and Szegö kernels

Kraußhar

2021

Math Methods in App Sciences

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Very recently one has started to study Bergman and Szegö kernels in the setting of octonionic monogenic functions. In particular, explicit formulas for the Bergman kernel for the octonionic unit ball and for the octonionic right half‐space as well as a formula for the Szegö kernel for the octonionic unit ball have been established. In this paper, we extend this line of investigation by developing explicit formulas for the Szegö kernel of strip domains of the form from which we derive by a limit argument considering d → ∞ the Szegö kernel of the octonionic right half‐space. Additionally, we set up formulas for the Bergman kernel of such strip domains and relate both kernels with each other. In fact, these kernel functions can be expressed in terms of onefold periodic octonionic monogenic generalizations of the cosecant function and the cotangent function, respectively.

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Towards Discrete Octonionic Analysis

Kraußhar

Legatiuk

2023

Springer Proceedings in Mathematics &Amp; Statistics

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SO(9,1) Group and Examples of Analytic Functions

Cited by 7 publications

References 4 publications

Conformal Mappings Revisited in the Octonions and Clifford Algebras of Arbitrary Dimension

Conformal Mappings Revisited in the Octonions and Clifford Algebras of Arbitrary Dimension

Recent and new results on octonionic Bergman and Szegö kernels

Towards Discrete Octonionic Analysis

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