科研之友
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摘要
Let be the ring of Laurent polynomials in commuting variables. As a generalization of the toroidal Lie algebra, the gradation shifting toroidal Lie algebra is isomorphic to the corresponding (centerless) toroidal Lie algebra so(n, C) circle times A of type B or D as a vector space, with the Lie bracket twisted by n fixed elements E-1, ... ,E-n from A. In this paper, we study the automorphisms of the gradation shifting toroidal algebra , which is proved to be closely related to a class of subgroups of GL(n, Z), called the linear groups over semilattices. We use the linear group over a special semilattice to determine the automorphism group of the gradation shifting toroidal algebra , which extends our earlier work.
