Relationship between Symmetric Brace Algebras and Pre-Lie Algebras

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dc.contributor.advisor E. Stitzinger, Committee Member en_US
dc.contributor.advisor A. Fauntleroy, Committee Member en_US
dc.contributor.advisor R. Martin, Committee Member en_US
dc.contributor.advisor T. Lada, Committee Chair en_US Hillman, Rebecca Ann en_US 2010-04-02T18:49:27Z 2010-04-02T18:49:27Z 2006-04-27 en_US
dc.identifier.other etd-03292005-215238 en_US
dc.description.abstract In this paper, we review the definitions of brace algebras, symmetric brace algebras, and pre-Lie algebras. We also look at a few examples of the calculations used in the brace algebra relations. We discuss the results of other mathematicians in these fields and where the topic of symmetric brace algebras is used. We then show a direct proof that a symmetric brace algebra is isomorphic to a pre-Lie algebra, using only the definitions. Showing that a symmetric brace algebra yields a pre-Lie algebra is very straightforward. However, the converse, a pre-Lie algebra yields a symmetric brace algebra, is not obvious. This paper uses an inductive proof to show the symmetry holds and that the brace is well-defined. Combinatorics plays a large factor in showing the brace is well-defined, along with identifying and classifying terms in a relation with m+n variables. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject Brace Algebra en_US
dc.subject Pre-Lie Algebra en_US
dc.subject Symmetric Brace Algebra en_US
dc.title Relationship between Symmetric Brace Algebras and Pre-Lie Algebras en_US PhD en_US dissertation en_US Mathematics en_US

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