On algebras and triangle relations

R.J. Lawrence

Abstract: Group and algebra structures have historically always had very close ties with geometric concepts. In this paper it is seen how, by imitating in higher dimensions, geometric structures arising naturally out of ordinary algebras, a notion of higher algebras can be constructed. An example of such a structure is given using quantum groups. The geometrical nature of these higher algebras is seen to provide natural settings for both Turaev & Viro's construction of three-manifold invariants, and higher versions of the Yang-Baxter relation.

Keywords: higher algebra structures, manifold invariants, Yang-Baxter equation, quantum groups, polyhedral decompositions

AMS subject classification: 57Q05 17A30

Length: 19 pages

Reference: `Proc. 2nd. Int. Conf. on Topological and Geometric Methods in Field Theory, Turku, FINLAND, 26th May-1st June, 1991.' Eds. J. Mickelsson, O. Pekonen, World Scientific (1992) 429-447 MR1224297 (94e:57032) (review by Sergej V. Matveev .)

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Last updated on March 18th, 2006.