Group Actions, Subgroups, Quotients, and Products

Guerino Mazzola; Maria Mannone; Yan Pang

doi:10.1007/978-3-319-42937-3_19

Group Actions, Subgroups, Quotients, and Products

Guerino Mazzola, Maria Mannone, Yan Pang

Music (Twin Cities)

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In musical creativity, actions are very important. They always deal with two components: the agent who acts in a determined way, and the object on which this action is being performed. Of course, not just any action can be performed on any object, so one has to specify agent/action as well as domain of objects that are suitable for a determined action. In this chapter we develop the formalism of group actions and provide introductory examples.

Original language	English (US)
Title of host publication	Computational Music Science
Publisher	Springer Nature
Pages	151-162
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-319-42937-3_19
State	Published - 2016

Publication series

Name	Computational Music Science
ISSN (Print)	1868-0305
ISSN (Electronic)	1868-0313

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Coset Representative
Group Homomorphism
Left Coset
Neutral Element
Quotient Group

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10.1007/978-3-319-42937-3_19

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AU - Mannone, Maria

AU - Pang, Yan

PY - 2016

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AB - In musical creativity, actions are very important. They always deal with two components: the agent who acts in a determined way, and the object on which this action is being performed. Of course, not just any action can be performed on any object, so one has to specify agent/action as well as domain of objects that are suitable for a determined action. In this chapter we develop the formalism of group actions and provide introductory examples.

KW - Coset Representative

KW - Group Homomorphism

KW - Left Coset

KW - Neutral Element

KW - Quotient Group

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PB - Springer Nature

ER -

Group Actions, Subgroups, Quotients, and Products

Abstract

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Keywords

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