Invariants of Finite and Discrete Group Actions via Moving Frames

Peter J. Olver

doi:10.1007/s41980-023-00744-0

Invariants of Finite and Discrete Group Actions via Moving Frames

Peter J. Olver

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear, is proposed. The resulting fundamental invariants are piecewise analytic and endowed with a rewrite rule that enables one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function thereof. The construction is inspired by the method of equivariant moving frames for Lie group actions.

Original language	English (US)
Article number	11
Journal	Bulletin of the Iranian Mathematical Society
Volume	49
Issue number	2
DOIs	https://doi.org/10.1007/s41980-023-00744-0
State	Published - Apr 2023

Bibliographical note

Funding Information:
I would like to thank Christoph Ortner for a lecture delivered at the University of Minnesota, supported by the Ordway endowment, that inspired this work and further discussions about the potential applications to computational chemistry. Thanks are also due to Misha Kapovich, who wrote the Theorem in [1], and Gregor Kemper and Francis Valiquette for helpful remarks and corrections.

Publisher Copyright:
© 2023, The Author(s) under exclusive licence to Iranian Mathematical Society.

Publisher link

10.1007/s41980-023-00744-0

Find It

Find It at U of M Libraries

Cite this

@article{f5047dbc79ac4bf69c173594add710be,

title = "Invariants of Finite and Discrete Group Actions via Moving Frames",

abstract = "A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear, is proposed. The resulting fundamental invariants are piecewise analytic and endowed with a rewrite rule that enables one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function thereof. The construction is inspired by the method of equivariant moving frames for Lie group actions.",

author = "Olver, {Peter J.}",

note = "Funding Information: I would like to thank Christoph Ortner for a lecture delivered at the University of Minnesota, supported by the Ordway endowment, that inspired this work and further discussions about the potential applications to computational chemistry. Thanks are also due to Misha Kapovich, who wrote the Theorem in [1], and Gregor Kemper and Francis Valiquette for helpful remarks and corrections. Publisher Copyright: {\textcopyright} 2023, The Author(s) under exclusive licence to Iranian Mathematical Society.",

year = "2023",

month = apr,

doi = "10.1007/s41980-023-00744-0",

language = "English (US)",

volume = "49",

journal = "Bulletin of the Iranian Mathematical Society",

issn = "1018-6301",

publisher = "Iranian Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Invariants of Finite and Discrete Group Actions via Moving Frames

AU - Olver, Peter J.

N1 - Funding Information: I would like to thank Christoph Ortner for a lecture delivered at the University of Minnesota, supported by the Ordway endowment, that inspired this work and further discussions about the potential applications to computational chemistry. Thanks are also due to Misha Kapovich, who wrote the Theorem in [1], and Gregor Kemper and Francis Valiquette for helpful remarks and corrections. Publisher Copyright: © 2023, The Author(s) under exclusive licence to Iranian Mathematical Society.

PY - 2023/4

Y1 - 2023/4

N2 - A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear, is proposed. The resulting fundamental invariants are piecewise analytic and endowed with a rewrite rule that enables one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function thereof. The construction is inspired by the method of equivariant moving frames for Lie group actions.

AB - A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions, both linear and nonlinear, is proposed. The resulting fundamental invariants are piecewise analytic and endowed with a rewrite rule that enables one to immediately express any other invariant (polynomial, rational, smooth, analytic, etc.) as a function thereof. The construction is inspired by the method of equivariant moving frames for Lie group actions.

UR - http://www.scopus.com/inward/record.url?scp=85148342022&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85148342022&partnerID=8YFLogxK

U2 - 10.1007/s41980-023-00744-0

DO - 10.1007/s41980-023-00744-0

M3 - Article

AN - SCOPUS:85148342022

SN - 1018-6301

VL - 49

JO - Bulletin of the Iranian Mathematical Society

JF - Bulletin of the Iranian Mathematical Society

IS - 2

M1 - 11

ER -

Invariants of Finite and Discrete Group Actions via Moving Frames

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this