Operads and special algebras

Rehren, Felix Gabriel (2012). Operads and special algebras. University of Birmingham. M.Phil.

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Abstract

We review the basic theory of operads, some variations thereof and other relevant constructions, including algebras over operads. The free operad is constructed from
first principles.

We define spheres with tubes and the sewing product, a way of composing the spheres with tubes. This has the structure of an operad and several subsets have other algebraic structures that we consider.

Spheres with tubes were used by Yi-Zhi Huang to study vertex operator algebras. We cover some of the relevant work to look at the relation they hold to the operad of
spheres with tubes and consider generalisations both of this operad and of operads generally.

Type of Work:	Thesis (Masters by Research > M.Phil.)
Award Type:	Masters by Research > M.Phil.
Licence:
College/Faculty:	Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department:	School of Mathematics
Funders:	None/not applicable
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
URI:	http://etheses.bham.ac.uk/id/eprint/3523

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