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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 4 | Year 2021 | Article Id. IJMTT-V67I4P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I4P508

Function Theory in Exotic Clifford Algebras and its Applications


Nguyen Thi Huyen, Doan Thanh Son
Citation :

Nguyen Thi Huyen, Doan Thanh Son, "Function Theory in Exotic Clifford Algebras and its Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 4, pp. 51-61, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I4P508

Abstract

In this paper, we will introduce Exotic Clifford algebras, whose structure relations are e2j+ej+αj = 0 and eiej+ejei+ei+ej =0. From this structure, we will present Cauchy integral formula. Moreover, boundary value problems for regular functions taking value in Exotic Clifford algebras can be solved in some low-dimensional cases.

Keywords
Exotic Clifford Algebras
References

[1] D. Alayon-Solarz and C. J. Vanegas, Operators Associated to the Cauchy-Riemann Operators in Eliptic Complex Number, Adv. Appl. Clifford Algebras 22 (2012) 257-270.
[2] The Cauchy – Pompeiu representation formula in eliptic complex numbers. Complex Variables and Eliptic Equations, 57(2012).
[3] D. Gilbarg and N.S. Trudinger, Eliptic Partial Differential Equations of Second Order, Springer-Verlag Berlin Heidelbaerg New York Tokyo (1983).
[4] Dao Viet Cuong, Trinh Xuan Sang, Function Theory in Clifford algebras Depending on Parameters and its Application, Journal of Mathematical Application, 16(1)(2018) 19-36.
[5] F. Brack, R. Delanghe and F. Sommen, Clifford Analysis, Pitman Research Notes in Mathematics, 76(1982).
[6] C. Miranda, Partial Differential Equations of Eliptic Type – Verlag New York, Heidelbaerg, Berlin (1970).
[7] W. Tutschke, Generalized analytic function in higher dimensions. Georgian Math. J. (2007) 581-595.
[8] The Distinguishing Boundary for Monogenic Functions of Clifford Analysis, Adv. Appl. Clifford Algebras 25(2015) 441-451.
[9] W. Tutschke and C. J. Vanegas, Clifford Algebras Depending on Parameters and Their Applications to Partial Differentiability Equations, chapter 14 in Some Topic on Value Distribution and Differentiability in Complex and P-adic Analysis, A. Escassut, W. Tutschke, and C. C. Yang, Science Press, Beijing (2008) 430-450.
[10] Yaglom. I. M, Complex Numbers in Geometry, Academic Press, New York, (1968).

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