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On the depth of separating algebras for finite groups

Abstract

Consider a finite group G acting on a vector space V over a field \({{\Bbbk}}\) of characteristic p >  0. A separating algebra is a subalgebra A of the ring of invariants \({{{\Bbbk}[V]^G}}\) with the same point separation properties. In this article we compare the depth of an arbitrary separating algebra with that of the corresponding ring of invariants. We show that, in some special cases, the depth of A is bounded above by the depth of \({{{\Bbbk}[V]^G}}\) .

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Correspondence to Jonathan Elmer.

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Elmer, J. On the depth of separating algebras for finite groups. Beitr Algebra Geom 53, 31–39 (2012). https://doi.org/10.1007/s13366-011-0030-1

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Keywords

  • Invariant theory
  • Separating algebra
  • Depth
  • Modular representation theory
  • Cohomology modules

Mathematics Subject Classification (2000)

  • 13A50 (Actions of groups on commutative rings; invariant theory)