Properties of functions associated with invariant theory

Autor:	H. E. A. Campbell, R. B. Bell, I.P. Hughes
Rok vydání:	1994
Předmět:	Discrete mathematics symbols.namesake Ring (mathematics) Algebra and Number Theory Invariant polynomial Polynomial ring symbols Regular representation Polarization of an algebraic form Algebraically closed field Invariant theory Hilbert–Poincaré series Mathematics
Zdroj:	Communications in Algebra. 22:381-396
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927879408824855
Popis:	We consider the ring of invariants RG obtained by letting a finite group G act via its regular representation on a polynomial ring with indeterminates over an algebraically closed field of characteristic zero. We note that the Hilbert series of RG can be thought of as a function of a certain sequence, namely the order structure of G. We consider properties of this and a related function for more general classes of sequences. As a result of our findings, we use invariant theory to give new proofs of two theorems, both originally due to Probenius, on finite groups.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::1a278e9dd2846f73ff38613f6121bb00 https://doi.org/10.1080/00927879408824855 Zobrazit plný text záznamu