This article is cited in 2 papers

Research Papers

Gröbner–Shirshov bases of the Lie algebra $B_n^+$

A. N. Koryukin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The minimal Gröbner–Shirshov bases of the positive part $B_n^+$ of the simple finite-dimensional Lie algebra $B_n$ over an arbitrary field of characteristic $0$ are calculated, for the generators associated with simple roots and for an arbitrary ordering of these generators (i.e., an arbitrary one of $n!$ Gröbner–Shirshov bases is chosen and studied). This is a completely new class of problems; till now this program was carried out only for the Lie algebra $A_n^+$. The minimal Gröbner–Shirshov basis of the Lie algebra $B_n^+$ was calculated earlier by Bokut and Klein, but this was done for only one ordering of generators.

Received: 29.01.2007

 English version: St. Petersburg Mathematical Journal, 2009, 20:1, 65–94

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