Generalized F-signature of invariant subrings

Mitsuyasu Hashimoto; Yusuke Nakajima

Generalized F-signature of invariant subrings

Commutative Algebra 2015-08-06 v4 Representation Theory

Authors: Mitsuyasu Hashimoto , Yusuke Nakajima

Abstract

It is known that a certain invariant subring $R$ has finite $F$ -representation type. Thus, we can write the $R$ -module ${}^eR$ as a finite direct sum of finitely many $R$ -modules. In such a decomposition of ${}^eR$ , we pay attention to the multiplicity of each direct summand. For the multiplicity of free direct summand, there is the notion of $F$ -signature defined by C. Huneke and G. Leuschke and it characterizes some singularities. In this paper, we extend this notion to non free direct summands and determine the explicit values of them.

Keywords

f-signature invariant subrings f-representation type direct sum decomposition singularities multiplicity

Cite

@article{arxiv.1311.5963,
  title  = {Generalized F-signature of invariant subrings},
  author = {Mitsuyasu Hashimoto and Yusuke Nakajima},
  journal= {arXiv preprint arXiv:1311.5963},
  year   = {2015}
}

Comments

9 pages, to appear in J. Algebra, v4:minor changes, v3:added some materials to Section 2 and Section 3, v2: by using the Brauer character, we improved the proof of the main theorem

Generalized F-signature of invariant subrings

Abstract

Keywords

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