Algebras and triangle relations

R. J. Lawrence*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper the new concept of an n-algebra is introduced, which embodies the combinatorial properties of an n-tensor, in an analogous manner to the way ordinary algebras embody the properties of compositions of maps. The work of Turaev and Viro on 3-manifold invariants is seen to fit naturally into the context of 3-algebras. A new higher dimensional version of Yang-Baxter's equation, distinct from Zamolodchikov's equation, which resides naturally in these structures, is proposed. A higher dimensional analogue of the relationship between the Yang-Baxter equation and braid groups is then seen to exhibit a similar relationship with Manin and Schechtman's higher braid groups.

Original languageAmerican English
Pages (from-to)43-72
Number of pages30
JournalJournal of Pure and Applied Algebra
Issue number1-3
StatePublished - 12 May 1995
Externally publishedYes

Bibliographical note

Funding Information:
*This work was supported in part by NSF Grant No. 9013738. 1T his paper was written while the author was a Junior Fellow of the Harvard Society of Fellows.


Dive into the research topics of 'Algebras and triangle relations'. Together they form a unique fingerprint.

Cite this