Cayley Theorems for Loday Algebras

Smith, Jonathan D. H.

doi:10.1007/s00025-022-01748-8

Results Math

2022

DOI: 10.1007/s00025-022-01748-8

|View full text |Cite

Cayley Theorems for Loday Algebras

Jonathan D. H. Smith

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Digroups are closely related to dimonoids [5] which also play an important role in problems from the theory of Leibniz algebras and they have been studied by many authors (see, e.g., [1,6,14,17]). One of the first results about digroups is the proof of the fact that Cayley's theorem for groups has an analogue in the class of all digroups [4].…”

mentioning

confidence: 99%

A new model of the free monogenic digroup

Zhuchok¹,

Pilz²

2023

Mat. Stud.

View full text Add to dashboard Cite

It is well-known that one of open problems in the theory of Leibniz algebras is to find asuitable generalization of Lie’s third theorem which associates a (local) Lie group to any Liealgebra, real or complex. It turns out, this is related to finding an appropriate analogue of a Liegroup for Leibniz algebras. Using the notion of a digroup, Kinyon obtained a partial solution ofthis problem, namely, an analogue of Lie’s third theorem for the class of so-called split Leibnizalgebras. A digroup is a nonempty set equipped with two binary associative operations, aunary operation and a nullary operation satisfying additional axioms relating these operations.Digroups generalize groups and have close relationships with the dimonoids and dialgebras,the trioids and trialgebras, and other structures. Recently, G. Zhang and Y. Chen applied themethod of Grobner–Shirshov bases for dialgebras to construct the free digroup of an arbitraryrank, in particular, they considered a monogenic case separately. In this paper, we give a simplerand more convenient digroup model of the free monogenic digroup. We construct a new classof digroups which are based on commutative groups and show how the free monogenic groupcan be obtained from the free monogenic digroup by a suitable factorization.

show abstract

mentioning

confidence: 99%

A new model of the free monogenic digroup

Zhuchok¹,

Pilz²

2023

Mat. Stud.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Cayley Theorems for Loday Algebras

Cited by 1 publication

References 29 publications

A new model of the free monogenic digroup

A new model of the free monogenic digroup

Contact Info

Product

Resources

About