A graph theoretic method for determining generating sets of prime ideals in quantum matrices

作者：Casteels Karel^*

来源：Journal of Algebra, 2011, 330(1): 188-205.

DOI：10.1016/j.jalgebra.2010.12.032

• Quantum matrices
• Graph theory

We take a graph theoretic approach to the problem of finding generators for those prime ideals of O-q (M-m,M-n(K)) which are invariant under the torus action (K*)(m+n). Launois (2004) [15] has shown that the generators consist of certain quantum minors of the matrix of canonical generators of O-q(M-m,M-n(K)) and in Launois (2004) [14] gives an algorithm to find them. In this paper we modify a classic result of Lindstrom (1973) [17] and Gessel and Viennot (1985) [6] to show that a quantum minor is in the generating set for a particular ideal if and only if we can find a particular set of vertex-disjoint directed paths in an associated directed graph.

• 出版日期2011-3-15