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Lie Algebras in Braided Monoidal Categories
Karlstad University, Faculty of Technology and Science.
2006 (English)Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
Abstract [en]

We begin by recalling some basic definitions from Lie algebra theory to motivate our subsequent transition to the more general setting of category theory. Next, we develop a relatively self-contained introduction to those areas of category theory needed for an understanding of what follows. Here we also motivate and introduce the graphical calculus notations. We then state the definitions of a braided commutator algebra, a braided Lie algebra, and a braided commutator Lie algebra. We proceed to show that color Lie algebras and Lie superalgebras are examples of braided Lie algebras. Thus, we are interested in examining color Lie algebras and Lie superalgebras in the generalized setting of braided Lie algebras. So we end by examining the representation theory of braided Lie algebras and braided commutator Lie algebras. In paricular, we find analogues of the adjoint representation, the tensor product representation, and the contragredient representation.

Place, publisher, year, edition, pages
2006. , p. 39
Keywords [en]
Physics
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kau:diva-397OAI: oai:DiVA.org:kau-397DiVA, id: diva2:6050
Presentation
2006-06-27
Uppsok
fysik/kemi/matematik
Supervisors
Examiners
Available from: 2006-09-12 Created: 2006-09-12

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Citation style
  • apa
  • harvard1
  • ieee
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  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
  • rtf