A gluing construction for polynomial invariants

作者：Huang Jia^*

来源：Journal of Algebra, 2011, 328(1): 432-442.

DOI：10.1016/j.jalgebra.2010.09.010

• Polynomial gluing
• Ring of invariants
• Sparsity groups

We give a polynomial gluing construction of two groups G(X) subset of GL(l, F) and G(Y) subset of GL(m, F) which results in a group G subset of GL(l + m, F) whose ring of invariants is isomorphic to the tensor product of the rings of invariants of G(X) and G(Y). In particular, this result allows us to obtain many groups with polynomial rings of invariants, including all p-groups whose rings of invariants are polynomial over F-p. and the finite subgroups of GL(n, F) defined by sparsity patterns, which generalize many known examples.

• 出版日期2011-2-15