# On multidimensional analogs of Melvin's solution for classical series of Lie algebras

*A.A. Golubtsova*^{1} and V.D. Ivashchuk^{2}

(1) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Miklukho-Maklaya St. 6, Moscow 117198, Russia

(2) Institute of Gravitation and Cosmology, Peoples' Friendship University of Russia, Miklukho-Maklaya St. 6, Moscow 117198, Russia

### Abstract

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra *G* is presented. The gravitational model contains *n* 2-forms and *l* ³ *n* scalar fields, where *n* is the rank of *G*. The solution is governed by a set of *n* functions obeying *n* ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating these polynomials for classical series of Lie algebras is suggested. The polynomials corresponding to the Lie algebra *D*_{4} are obtained. It is conjectured that the polynomials for *A*_{n}-,*B*_{n}- and *C*_{n}- series may be obtained from polynomials for *D*_{n+1}-series by using certain reduction formulas.

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