Palabras clave
vector product
Leibniz formula
álgebra de Clifford
producto de vectores
fórmula de Leibniz
Cómo citar
Resumen
Las álgebras de Clifford son álgebras asociativas y no conmutativas definidas a través de ciertas estructuras multiplicativas. En estas álgebras no siempre existe una fórmula explícita que permita expresar el producto entre los vectores de la base del espacio vectorial, tal como está propuesto en el álgebra An (ver [6]). En esta investigación se ofrece una expresión explícita para el producto de determinados elementos de la base del álgebra An(2, αj , γij ), lo cual representa la apertura para deducir cálculos que arrojen nuevos aportes en el análisis de Clifford con parámetros.
Citas
E. Ariza, A. Di Teodoro, M. Sapiain, F. Vargas, Sufficient conditions for first-order differential operators to be associated with a q-metamonogenic operator in a Clifford type algebra, Comput. Methods Funct. Theory 17(2017), no. 2, 211–236. Doi: 10.1007/s40315-016-0182-y
E. Ariza, J. Vanegas, F. Vargas, First order differential operators associated to the space of monogenic functions in parameter-depending Clifford algebras, Adv. Appl. Clifford Algebras 26(2016), no. 1, 13–29. Doi: 10. 1007/s00006 015-0577-2
Y. Bolívar, Problemas de valores iniciales en análisis de Clifford generalizado. Tesis de Doctorado, Universidad Central de Venezuela, Caracas, Venezuela, 2013.
Y. Bolívar, L. Lezama, L. Mármol, C. Vanegas, Associated spaces in Clifford analysis, Adv. Appl. Clifford Algebras 25(2015), 539–551. Doi: 10.1007/s00006-015-0528-y
Y. Bolívar, C. Vanegas, Initial value problems in Clifford-type analysis, Complex Variables and Elliptic Equations 58(2013), no. 4, 557–569. Doi:10.1080/17476933.2012.697458
F. Brackx, R. Delanghe, F. Sommen, Clifford Analysis. Research Notes in Mathematics 76, Pitman Books Ltd., Boston MA, 1982.
R. Heersink, W. Tutschke, Solution of initial value problems in associated spaces, in: W. Tutschke & A.S. Mshimba (Eds.) Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations (Trieste, Italia 1993). World Sci. Publ., Singapore, 1995, pp. 209–219. Doi:10.1142/2927
N.Q. Hung, Initial value problems in Quaternionic analysis with a disturbed Dirac operator, Adv. Appl., Clifford Algebras 22(2012), no. 4, 1061–1068. Doi: 10.1007/s00006-012-0332-x
N.Q. Hung, N.C. Luong, First order differential operators associated to the Dirac operator of quaternionic analysis, in: Methods of Complex and Clifford Analysis, Proceedings of ICAM (Hanoi, 2004), SAS International Publications, Delhi, 2006, pp. 369–378.
L.H. Son, N.Q. Hung, The initial value problems in Clifford and Quaternion analysis, in: Proceedings of the 15th ICFIDCAA 2007, Osaka, Japan, Municipal Universities Press 3, 2008, pp. 317–323.
L.H. Son, W. Tutschke, Complex methods in higher dimensions. Recent trends for solving boundary value and initial value problems, Complex Var. Theory Appl 50(2005), no. 7-11, 673–679. Doi: 10.1080/ 02781070500087600
W. Tutschke, Associated spaces - A new tool of real and complex analysis, in: Function Spaces in Complex and Clifford Analysis, National University Publishers, Hanoi, Vietnam, 2008, pp. 253–268.
J. Vanegas, F. Vargas, Associated Operators to the Space of Meta-q-Monogenic Functions, in: P. Cerejeiras, C.A. Nolder, J. Ryan, C.J. Vanegas Espinoza (Eds.) Clifford Analysis and Related Topics, Springer Proceedings in Mathematics & Statistics, Springer Nature Switzerland AG, 2018, pp. 141-152. Doi: 10.1007/978-3-030-00049-3-8