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

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).