A question about index notation

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Discussion Overview

The discussion revolves around the interpretation of index notation, specifically the expression B_{[ij} B'_{kl]} where B and B' are bivectors. Participants explore the implications of antisymmetrization in this notation as found in a referenced paper.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks clarification on the meaning of the notation B_{[ij} B'_{kl]} in the context of bivectors.
  • Another participant explains that the notation indicates that the expression is antisymmetrized across all indices.
  • A participant questions whether indices outside the brackets are antisymmetric with those inside, suggesting a distinction in treatment.
  • A later reply confirms that indices outside the brackets are not antisymmetric with those inside.

Areas of Agreement / Disagreement

Participants generally agree on the antisymmetrization aspect of the notation, but there is some uncertainty regarding the treatment of indices outside the brackets.

Contextual Notes

The discussion does not resolve the implications of the notation fully, and assumptions about the context of bivectors and their properties remain implicit.

naima
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Could you please tell me what means
[tex]B_{[ij} B'_{kl]}[/tex] where B and B' are bivectors
I found it in http://arxiv.org/abs/hep-th/0311162"
look at lemma 2.4
thanks
 
Last edited by a moderator:
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hi naima! :smile:

it means the whole thing is antisymmetrised in all indices …

the indices are treated the same way as in [itex]A_{[ijkl]}[/itex] :wink:
 
ok thanks
And I guess when one is outside the brakets it is not antisymmetric with those inside?
I'll go on reading this paper it seems interesting.
 
naima said:
And I guess when one is outside the brakets it is not antisymmetric with those inside?

yup! :smile:
 

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